Follow one scalar through every layer.
Compare adjacent stages, inspect the XOR signature, and test the exact curve mirror k ↔ n−k.
One reproducible point in the book.
The Pair Lab example is saved in hexadecimal. Use its verified point and page to check navigation and curve transformations. Its QR pairing score does not assign probabilities to other pages.
Verifying the reference point…
- SCALAR · HEXADECIMAL
- —
- SCALAR · DECIMAL
- —
- PAGE · 1,000 KEYS
- —
- LINE
- —
- COMPRESSED PUBLIC POINT
—
Six QR projections of the same key
Each square is a standards-based QR code using fixed M error correction. Hover to inspect; click a card to pin it.
XOR / difference matrix
Curve mirror laboratory
(n−k)G = −kG. The X coordinate is identical, Y is reflected across the field, and the compressed SEC prefix flips between 02 and 03. HASH160 then destroys that visible relation.
Derive a scalar to measure its mirror pairing.
Find the most completely paired mirror signature.
The experiment first exhausts all 36 unordered QR-mask combinations. It then searches a bounded scalar interval for keys whose natural masks reach the proven ceiling.
0x743186…53218Ready
No candidate measured.Gold marks exact isolated pairs, red marks singletons, and cyan marks larger connected components.
| Rank | Scalar | Masks | Changed | Exact pairs | Exact-pair coverage | Neighbor coverage | Singletons | |
|---|---|---|---|---|---|---|---|---|
| Start a bounded scan to rank candidate scalars. | ||||||||
Inspect all 36 mask-pair templates
| Rank | Masks | Changed | Exact pairs | Exact-pair coverage | Neighbor coverage | Singletons | Large-cluster cells |
|---|---|---|---|---|---|---|---|
| Building atlas… | |||||||
Interpretation boundary: under lowercase compressed-SEC hex, QR byte mode, error correction M, and version 5, no scalar can produce 100% isolated pairs. A scalar changes which masks the encoder selects; it does not change the signature belonging to that mask pair.
What this instrument can—and cannot—show
It can reveal exact transformations that survive from one representation to the next, including the secp256k1 point-negation symmetry.
It cannot reverse HASH160 or infer a private page from an address image. A visually close final matrix is not “warmer” cryptographically.
The square pond
Choose one of the scalar’s 32 bytes and disturb it. The model first forecasts where the sand should move from nearby basis ripples, then reveals the independently measured movement through every stage.
Cyan is forecast movement. Gold is measured movement.
WIF and SEC are parallel representations derived from the scalar; the ribbon orders them for comparison. The QR stage uses the encoder’s selected mask, so a mask change can create an additional whole-grid jump.
Sensitivity map
Run one controlled low-bit disturbance at every scalar byte. Each row is an input byte; each column measures how much sand actually moved at a later stage.
Structure carries
The scalar and WIF payload retain direct byte position, so the model can forecast their movement sharply.
The curve mixes
SEC and X respond deterministically, but a nearby scalar disturbance spreads across the point coordinates.
The hash becomes surf
At HASH160 and the address QR, prediction is statistical: roughly half the bits move, without a directional path back to the source.
The 4D Book
One cryptographic disturbance supplies the measured forcing field. Seven square fluid pages carry it through transformation depth while time advances the water and moves sediment across each bottom.
Hydrodynamic depth stack
Water carries the signal; sediment records its passage.
The solver uses a finite-difference shallow-water approximation with viscosity, bottom drag, erosion, deposition, and delayed coupling between stage-depth pages.
∂h/∂t + ∇·(h u) = 0∂u/∂t = −g∇η + ν∇²u − r u∂b/∂t = deposition − erosionF(z,t) = XOR(z) · pulse(t−τz)The XOR fields are real Bitcoin transformation measurements. Here “4D” means X/Y square position, seven discrete stage-depth pages Z, and simulation time T. The water, viscosity, erosion, and sediment are an exploratory coordinate system—not physical forces inside secp256k1 and not a method for reversing HASH160.
Search a stated interval without losing your place.
Parse a full SEC point, HASH160, or supported Bitcoin address; run an exact bounded search or classical kangaroo walk; and carry progress through a SHA-256 checked checkpoint.
Ready
———No result yet.CPUkang browser monitor initialized.
Measure this browser
Derives only the public test range beginning at scalar 1. It never accepts or compares a wallet target.
No benchmark run.
Build a real CPU oracle window
Checks a bounded page classically, then plots ideal Grover probability. This is a simulator—not quantum hardware or a speedup.
No oracle window built.
Load a local list
Classic mainnet P2PKH rows become HASH160 targets. P2SH rows are validated references only. Nothing is uploaded.
Native acceleration stays native
The Python application’s SQLite catalog, multiprocessing pool, filesystem logs, and optional RCKangaroo GPU launch cannot run inside a static Site. Their browser equivalents here are bounded, in-memory, and explicitly user-started.
Rank broad bands, then schedule metadata only.
Import solved-puzzle rows. Each row is cryptographically verified before it influences the transparent position prior. The schedule never generates candidate keys.
No solved CSV loaded.
| Rank | Band | Normalized position | Empirical mass | Key interval | Book pages |
|---|---|---|---|---|---|
| Import a compatible solved-puzzle CSV. | |||||
No range schedule built.
Measure the hunch against a baseline.
Compare the position prior, a QR-mask-conditioned variant, and a uniform starting window. All three receive the same coverage allowance. Optional timed trials check real public points and include the cost of ranking and target QR analysis.
Ready. The benchmark does not change search ranges or page-model scores.
| Method | Coverage hits | Uniform expected hits | Timed search hits | Points checked | Total ranking time |
|---|---|---|---|---|---|
| Start a test to measure each method. | |||||
Coverage hits count targets lying inside the selected exact intervals; they do not mean those intervals were exhaustively searched. Timed search hits are verified public-point matches.
Experiment rules and interpretation
The position prior uses the same rule as the page model above. The QR variant groups training points by their two natural QR masks. With at least three matching training rows, it blends that group's prior 50/50 with the overall prior; otherwise it falls back to the overall prior. These settings are fixed before testing.
Each predictor sees a test public point and its bounds. Its private scalar is reserved for scoring. Imported tests use only strictly smaller-bit rows for training; synthetic training and test keys are disjoint. QR features require the full public point.
The time budget includes target feature extraction, model fitting, ranking, and actual point checks. Reusable training-feature preparation is reported separately. A batch already in flight can overrun the timer; points checked after the deadline are not counted. Method order rotates between targets.
A small or favorable sample does not establish a shortcut for an unsolved puzzle. Export the results, repeat with different seeds, and compare held-out solved rows. No benchmark result automatically changes an active search.
The Wormhole Keybook
Two exact descriptions meet at one verified curve point. Scalar pages remain fixed; coordinate-index pages reflect only the points saved in this browser.
Q − cⱼG = ±iGcandidate k = cⱼ ± iGenerate exact pages
Page 1 is ready to generate.
| Line | Scalar | Private hex | SEC compressed | X coordinate |
|---|---|---|---|---|
| Generate the page to build its verified coordinates. | ||||
Open the same point from either side
Select a scalar row or search the saved index.
| Index | X | Y | Scalar page | Line |
|---|---|---|---|---|
| The verified index is empty on this browser. | ||||
Suggest the first exact page
A 64-nibble mask uses hexadecimal characters and ? wildcards. Digit constraints are solved directly; no candidate keys are generated.
Move one point by an exact signed scalar distance.
Changing page or line changes the scalar by Δk. The curve bridge is exactly P₂ = P₁ + ΔkG; the return bridge uses −Δk.
1000@page 1 → 1@page 2References load when a search starts.
Let two curve descriptions collide.
Build iG for a bounded radius, then cross the interval in signed blocks. A reported scalar is accepted only after a fresh multiplication reproduces the target SEC.
Plan a full-point interval or load the 424242 demo.
No bridge plan yet.
Full SEC + bounded interval required.It is the exact equality of two elliptic-curve constructions, not physical wormhole behavior and not a shortcut through HASH160. Address and HASH160 targets can be checked exhaustively or looked up in points already saved to the coordinate index; they cannot enter the point bridge without the full curve point.
Anchor prediction
Test whether public-point similarity to measured anchors helps locate an unknown scalar.
An estimate is a hypothesis. Its page is exact for the proposed scalar, but it is not a verified location of the target. Run the comparison test before relying on a pattern.
Target and range
A public key enables the experimental estimate. An address enables an exact comparison with the recorded anchors only.
Uses exact integer bounds. No search starts automatically.
Ready for an experiment
The atlas includes your measured anchors and samples from widely separated regions.
- Page
- —
- Line
- —
- Scalar · hex
- —
- Candidate interval · inclusive
- —
- Target QR masks
- —
- Range fraction covered
- —
Loading the anchor atlas…
Keyspace atlas
Column heights show log-scaled record counts, not target probabilities. Mirrors are derived points, not additional scan coverage. Empty regions have no recorded anchors; they have not been eliminated.
| Scalar / source | Page / line | Natural masks | Navigation |
|---|
Sample distant regions
Scan one bounded window in each region. Only keys with the natural 0 ↔ 7 signature become anchors.
The default run checks 32,768 scalars spread across 16 regions. Pause and export to preserve its exact next positions.
Test unseen public keys
Generate independent test keys inside your chosen range. Compare equal-size candidate intervals, with each test scalar hidden from the predictor.
Test coverage is separate from the candidate interval width above. This measures prediction coverage, not search speed.
Prediction evidence
No benchmark has run for this atlas and range.
| Method | Targets covered | Hit rate · 95% interval | Median distance / range |
|---|---|---|---|
| Run the comparison to measure the hypothesis. | |||
Uniform selection, the fixed range midpoint, and a random anchor provide separate controls. One small test cannot establish an advantage on real puzzles.
Equation, supporting anchors, and limits
The model balances the atlas across 32 scalar regions, retaining up to four references per occupied region. It selects the eight references whose compressed public keys have the fewest differing bits from the target.
dᵢ = popcount(SEC(Q) XOR SEC(Aᵢ))wᵢ = floor(2⁴⁰ / (1 + dᵢ)²)estimated k = floor(Σ wᵢ aᵢ / Σ wᵢ)
This weighted scalar estimate is an experimental rule, with no established relation between public-key bit similarity and scalar distance. It is not derived from the curve group law. An exact public-key match to a verified anchor is reported separately.
The exact identities remain Q = A + dG and −Q = −A − dG, with scalar mirror n − k. Knowing A = aG does not make the unknown offset d available.
Imported anchors are checked against their scalars and the same QR encoder before use. Sampling and comparison use a background worker; nothing is sent to a blockchain service.
SEC 1: curve arithmetic and point encoding · SEC 2: secp256k1 parameters
Automatic
Enter what you know. Run the applicable tests in order and keep one report.
Known data
Additional known data
Additional fields describe the same target. Inconsistent data stops the run before searching.
Range and work limits
Plain digits are decimal. Prefix hexadecimal values with 0x. Search budgets apply separately to each method; they do not cover the whole keyspace.
All test budgets
Choose tests
Pause/resume stays in this tab. Export before closing. Loading a report restores its inputs for a fresh run.
Ready to run
READYEnter known data or load the public demo.
Inputs have changed. This report belongs to the previous run; run again to use the new data.
Verified target match
Only a scalar checked against the target appears here.
- Page
- —
- Line
- —
- Scalar
- —
Experimental candidate
Predictions appear separately and do not change your search bounds.
- Proposed page / line
- —
- Candidate interval
- —
Test sequence
Expand a row for its measurementsThe sequence uses the current verified Anchors atlas, saved coordinate index, and solved rows imported in CPU Lab. Pond/4D animations remain visual views; their disturbance measurements are included above. Predictions are hypotheses. A completed test is not a solved puzzle, and work counts from different methods can overlap.
One book. Every scale.
Rotate the sphere, enter its regions, and select a key to inspect its exact records. Move between the sphere and your original Keybook without retyping the scalar.
Opening the spherical book
The viewer loads locally when this tab is opened.
Camera zoom and keyspace depth are separate. Scroll or pinch to magnify; double-click a region to subdivide its exact interval. Star positions are a navigation layout, not cryptographic proximity. Key details and page locations expose private-key material; use research keys only.
Manual
Instructions for the Automatic edition, its individual labs, and the integrated 3D Sphere.
1. Quick start
Use Automatic to run the applicable tests from one set of known data. Use the other tabs to inspect a result or control a single experiment. Calculations run on your computer in the browser; an open site does not provide a remote search service.
- Open Automatic and choose Load demo.
- Leave the sample range and budgets in place, then select Run all selected tests.
- The known demo scalar is
424242. Its verified position is page 425, line 242. The report identifies it as supplied data. - Expand a test’s Measurements and exact values to inspect what was computed. Some tests will be skipped because the demo has no suitable data for them.
- Select Export report .txt for reading or Export report .json for the structured results and reusable input setup.
For your own experiment, replace the demo data with one target and its known range. Leave unknown fields blank. Clear the demo scalar before entering an unrelated address or public key.
Choose Puzzle 71 in Automatic. It fills address 1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU and the inclusive bounds 0x400000000000000000 through 0x7fffffffffffffffff. It does not supply the unknown public point or private scalar. Point-only tests therefore explain why they are skipped. This preset is input data, not a live check of the puzzle’s status or balance.
2. Inputs and number formats
Check the notation before running. In Automatic and Anchors, plain digits are decimal and hexadecimal numbers need an explicit 0x prefix. In Keybook, Pair Lab, CPU Lab and the Wormhole search, the relevant notation selector controls how numbers are read.
| Field | What to enter | What it enables |
|---|---|---|
| Target | One supported Bitcoin address, a 40-character hexadecimal HASH160, or a full SEC public key. | Exact comparison against candidates. An address/hash alone does not supply curve coordinates. |
| Public SEC key | Compressed: 66 hex characters beginning 02 or 03. Uncompressed: 130 hex characters beginning 04. | Curve, mirror, QR, point-search and experimental prediction tests. |
| X and Y | Both coordinates, each up to 64 hex digits. Leading zeroes may be omitted; 0x is optional here. | Reconstructs and validates a full curve point. X alone is insufficient in these fields. |
| Known scalar | For example, decimal 424242 or equivalent hexadecimal 0x67932. | Exact page/line, address derivation, mirror scalar and controlled byte disturbances. |
| Known page and line | Enter both: for the demo, page 425 and line 242. | Identifies an exact scalar. Do not use these fields for a guessed page. |
| Known key digits | Exactly 64 hexadecimal digits or ? wildcards, without a 0x prefix. Each wildcard represents one unknown hex digit. | Finds a mask-compatible position and constrains candidate acceptance. It does not by itself prove a target match. |
| Lower / upper scalar | Inclusive decimal or 0x bounds. In Automatic, blank lower means 1 and blank upper means n − 1. | Defines the permitted range. A work budget limits how much of it is processed. |
All supplied fields must describe the same target. The program checks agreement between the scalar, public point, address, page/line and known digits. A known scalar must lie inside your stated range.
743186643908653218 is decimal in Automatic. The recorded hexadecimal example is 0x743186643908653218, on page 2143390962501162448, line 384. Keep the prefix when copying that anchor into Automatic or Anchors.
Paste long integers as text. Avoid scientific notation, rounded spreadsheet values, separators and arithmetic expressions. A WIF is an output of the known-scalar derivation; it is not an accepted Automatic target or scalar input.
Automatic accepts the single-key address templates implemented in CPU Lab. P2SH comparisons assume nested P2SH-P2WPKH, and Taproot comparisons assume a key-only output with no script tree. Unsupported scripts cannot be identified from their address alone. Address columns produced by the derivation test are labelled as mainnet outputs.
3. Automatic workflow
- Enter known data. Give the run a name. Paste the target, then open Additional known data only for facts you possess. Use current key copies the scalar and point currently selected in Keybook.
- Set the range. Enter the lower and upper scalar. A smaller stated range does not become more likely merely because it is small.
- Set work limits. The main search budget applies separately to each search method. Open All test budgets for sampling, benchmark and table limits.
- Choose tests. All 18 are selected initially. Validation always runs. Tests keep their fixed order; a disabled prerequisite may cause a dependent test to be skipped.
- Run. Automatic takes a snapshot of the current atlas, saved coordinate index and solved rows already imported into CPU Lab. It then runs one selected test at a time.
- Inspect and export. Read each status and its details. Use Open in book for a verified result, or Inspect candidate for an explicitly unverified estimate.
Pause waits for the next checkpoint and keeps the current worker in this tab. Resume continues it. Stop ends the sequence and retains completed results and available partial counters. A stopped sequence has no resume control; starting again creates a fresh run. Inputs stay locked while running or paused.
Switching tabs is not the same as pausing. Keep the browser open while a run is active. Browser throttling or computer sleep can delay progress. A new Automatic run replaces the displayed report, so export anything you want to keep first.
| Setting | Default | Meaning |
|---|---|---|
| Search budget | 2,048 | Candidate positions for exhaustive checks; walk steps for kangaroo; giant lookups for Wormhole. Applied separately. |
| Pattern candidates | 128 | At most this many proposed pattern positions, with mask exclusions reported. |
| Natural-optimum samples | 256 across 8 regions | Total samples spread over the entered range. This differs from Anchors’ per-region setting. |
| Prediction trials | 32, at 10% coverage | Independent synthetic test targets with equal candidate coverage per method. |
| Bridge table entries | 512 | Caps the signed bridge’s reference table. It is separate from the giant-lookup budget. |
| Oracle qubits | 8 | Up to 256 classical candidate positions, clipped at the range end. Probabilities are simulated. |
| Benchmark derivations | 512 | Public-range point derivations and SEC encoding; excludes address hashing and QR scoring. |
Sampling, walk and test seeds make those parts repeatable with the same inputs and references. Timing still varies. Load setup from report restores inputs for a new run using the current references; it neither resumes a closed worker nor accepts imported results as verified.
4. The 18 Automatic tests
A public point or scalar found by exact recorded-data lookup can unlock later tests. Each row below describes one step; the result panel reports whether it ran, was skipped, stopped, or failed.
| Step | Required data | Result and interpretation |
|---|---|---|
| 1. Validate known data | Any accepted target or known-data combination. | Checks formats, bounds and consistency. A validation error prevents the remaining sequence. |
| 2. Anchor and saved-index lookup | A target, which may be an address/hash. | Compares recorded points, including anchor mirrors. Any matching scalar is freshly verified. This searches records, not the whole keyspace. |
| 3. Address chain and curve mirror | A full public point; scalar needed for WIF and exact pages. | Derives encodings and addresses, checks opposite Y and equal X, and reports known scalar/mirror positions. |
| 4. Known digits and book position | A 64-character key mask. | Finds the first compatible scalar in the range. A compatible page is not a verified target location. |
| 5. Natural QR mirror and same-mask control | A full public point. | Measures naturally selected masks and pair coverage; compares a forced same-mask control. |
| 6. All 36 QR mask-pair tests | A full public point. | Measures all unordered fixed-setting mask combinations and their best isolated-pair coverage. |
| 7. Pond / 4D disturbance measurements | A known or exactly matched scalar. | Measures 32 byte interventions through seven stages, plus a local held-out forecast. It does not run the water animation. |
| 8. Find natural optimums in the range | A valid range. | Samples bounded windows, records every natural 0 ↔ 7 hit and compares sampled candidates to the target when present. New anchors inform later tests in this run. |
| 9. Anchor page prediction | A public point and at least three independent anchor families in range, unless there is an exact known match. | Produces a heuristic interval, reports an exact lookup separately, or explains insufficient references. |
| 10. Prediction versus controls | Sufficient anchor families and unseen scalar positions. | Tests independent synthetic keys against uniform, midpoint and random-anchor controls. It measures coverage, not real-puzzle success. |
| 11. Check the proposed anchor interval | A heuristic interval from step 9. | Runs exact target checks inside the proposed interval. Selection is experimental; target verification is exact. The entered range is unchanged. |
| 12. Solved-puzzle bands and schedule | At least three suitable verified solved rows imported in CPU Lab. | Ranks descriptive bands and clips them to the entered range. Builds range metadata; does not check candidates. |
| 13. Bounded pattern candidates | A target and range. | Checks midpoint, boundary, repeated-digit and other defined candidates within its budget. |
| 14. Bounded exhaustive search | A target and range. | Visits a contiguous prefix from the lower bound, applies the key mask, and records the next scalar. Stops on a match, range completion or budget. |
| 15. Pollard kangaroo | A full public point. | Runs bounded classical walks and verifies any collision. A spent step budget is not exhausted keyspace. |
| 16. Signed Wormhole search | A full public point. | Checks signed baby/giant-step blocks. The report separates table size, giant lookups and interval completion. |
| 17. Classical oracle / Grover simulation | A target and range. | Checks the small window classically, then calculates ideal probabilities. It does not use quantum hardware or provide quantum speedup. |
| 18. CPU derivation benchmark | No target-specific data beyond a valid run setup. | Measures public point generation. Its points-per-second figure is not the speed of address matching or QR analysis. |
5. Reading results
| Result | Meaning |
|---|---|
| Verified target match | The scalar reproduces the target under the stated encoding/template and meets the supplied constraints. Read its sources to distinguish a supplied scalar, known-record lookup and a search result. |
| Experimental candidate | A proposed scalar and its exact book coordinates. These are not a verified location of the target. |
| Exact match excluded by constraints | A recorded match lies outside the entered range or conflicts with the key mask. It is reported separately for review. |
| Complete | That test finished its configured work. Read its details to learn whether it exhausted an interval, sampled it or only measured a property. |
| Skipped | The test was disabled, a prerequisite was missing, or validation/stop prevented it. Read the stated reason. |
| Budget reached / no match | No accepted result was found in the reported work. Unchecked positions remain unless the result explicitly says the entire interval was exhausted. |
| Error / stopped | The test did not finish normally. Completed results and recorded partial counters remain available. |
Counts from different methods can overlap. Do not add sampled scalars, pattern checks, oracle checks, walk steps and giant lookups together as unique coverage. Even an exhaustively checked interval only rules out a match within its stated bounds and constraints.
Editing Automatic inputs after a run marks its report stale and disables result navigation. Exports still describe the earlier input snapshot until you run again.
6. Keybook and exact navigation
Choose Notation, enter a valid private scalar and select Derive chain. The six cards display the scalar, compressed WIF, compressed SEC, X coordinate, HASH160 and P2PKH address. The difference panels compare their QR projections. Use − 1, + 1 or Mirror n−k to move from the current scalar.
The book contains 1,000 scalar positions per page. Page and line start at 1; the final page has 336 valid lines. Moving to a page does not imply that an unknown target is on that page.
- In Navigate from a reference anchor, enter an exact scalar using decimal or explicit
0x, then select Set anchor. You can also choose Use current scalar. - Enter a signed scalar offset
dand select Go to offset. The destination isk = a + d. Offsets are scalars, not pages. - Alternatively enter a page and line and choose Open page and line, or use the configured Step size.
- Flip book side changes the reference to
n − aand the position ton − k; the offset changes sign. Flipping twice returns to the starting position.
Navigation stops at the valid scalar boundaries rather than wrapping. A navigation anchor is a known reference scalar; it need not have the special natural QR-mask signature.
7. Natural optimum hits and the 3D book
In the Keybook tab, scroll to Find natural optimums. Set the center notation and scalar, a radius on each side, and the worker count. The radius is a decimal count of scalars. The interval is clipped at 1 and n − 1; a radius of 500 normally gives 1,001 candidates.
- Choose Scan full interval or Stop at first optimum, then Start new scan.
- Use Pause and Resume for the current scan. Worker count controls local browser workers, not external computers.
- Open View all optimum hits to inspect the complete hit list. Its pages display subsets; Export all hits (.txt) includes every recorded hit.
- Export before starting another scan or reloading. The hit list is not a file that resumes the old scan.
The fixed QR settings are lowercase compressed-SEC hexadecimal, Byte mode, M error correction and version 5. The best natural mask pair in this lab is 0 ↔ 7. Its isolated-pair coverage is about 48.65% of the changed modules. “Optimum” describes that scoring rule, not proximity to a puzzle key.
Open 3D book plots recorded hits by page offset, line and mask direction. Select the bundled 138-hit scan, the current scan or an imported hit TXT. Drag to rotate, use the rotation/tilt controls, and select a dot or the hit navigation buttons.
Book side switches between recorded scalars and their mirrors. Previous opposite mask and Next opposite mask visit recorded hits with the other direction. Use hit as navigation anchor transfers the selection to exact book navigation. Lines connecting dots join the chosen records; omitted gaps have not been proven empty.
8. Anchors and experimental prediction
The bundled atlas starts with 519 independent anchor families and 1,038 points when their mirrors are included. It combines measured hits from multiple regions; it is a sparse atlas, not a complete map of the keyspace.
- Enter a full SEC public key and range in Anchors. A mainnet P2PKH address instead enables exact comparison against recorded anchor addresses.
- Set Candidate interval width and select Estimate page. An exact known match, an unverified estimate, insufficient references and address-only data are distinct outcomes.
- Open proposed page inspects the proposed scalar. Prepare bounded search copies its point and interval into CPU Lab; it does not start searching. Pause an active CPU search before preparing a replacement.
- Use Compare with controls to test unseen synthetic points at equal interval coverage. Export the test results to retain the evidence.
The predictor balances references across scalar regions, compares compressed-SEC bit differences and calculates a weighted scalar mean. Its rule has not established a reliable relation between public-key similarity and scalar distance. The bundled 256-target test at 10% coverage found 27 hits for anchor projection, 23 for uniform selection, 29 for the midpoint and 21 for random-anchor selection; those results did not establish an advantage.
Extend and reuse the atlas
In Sample distant regions, select the whole valid keyspace or the chosen prediction range, then set regions, scalars per region and a seed. The Anchors default is 16 × 2,048 = 32,768 checks, unlike Automatic’s 256 total default samples. Sampling discovers and records natural-mask anchors within those bounded windows.
Choose Pause task, then Export atlas + checkpoint to preserve the atlas and sampling positions. Import that JSON and choose Resume paused scan to continue. A comparison benchmark can be exported as evidence, but does not use the sampling resume control.
Add current optimum hits imports the current Pair Lab results. Automatic’s Add hits to Anchors transfers its recorded hits. Imported scalars, points and QR masks are verified before use. Export all hits .txt also works with the 3D book importer.
The distribution bars show record counts, not target probabilities. Clicking a region changes the selected bounds. A mirror is a derived reference point, not another independently scanned scalar range.
9. Pond and 4D Book
Pond: byte sensitivity and forecasts
First select a scalar in Keybook. In Pond, select one of its 32 bytes: byte 00 is most significant and byte 31 is least significant. Choose a low/high-bit flip or an addition/subtraction at that byte’s weight, then select Forecast → reveal. Cyan represents forecast movement and gold represents the measured movement.
Map all 32 bytes measures controlled disturbances across Scalar, WIF raw, SEC, X, HASH160, Address and QR. The seven-stage order is a comparison view; WIF and SEC are parallel representations of the scalar. An intervention that leaves the valid scalar range cannot be used.
4D Book: visualize the same measured disturbance
Choose the scalar byte and bit, then select Launch ripple. Adjust gravity, viscosity, drag, erosion, deposition or coupling to explore the visual simulation. Use Pause, Step, Reset and the time section to inspect its state.
Here X/Y are positions in a square field, Z is transformation depth, and T is simulation time. The forcing comes from measured transformation differences; the fluid and sediment are a visualization model. Energy, sediment and visual resemblance are not probabilities of recovering a key.
10. CPU Lab
- Choose Target type or Auto detect, paste the target, and select the bounds notation.
- Enter inclusive bounds and choose Exhaustive or Pollard kangaroo. Kangaroo requires a full SEC public key; use exhaustive comparison for an address or HASH160.
- For HASH160 comparisons, choose compressed, uncompressed or both. For exhaustive order, choose forward or inward from both ends.
- Set Work budget / run and select Start new. Watch the checked count, remaining interval and verification message.
- Use Pause, then Export checkpoint before closing. Import that checkpoint in CPU Lab and select Resume to continue the saved session.
The optional kangaroo settings control walkers, collision-table size, pattern prepass and mirror collisions. An additional walker is a classical walk, not a guarantee of proportionally faster searching. Run safe benchmark measures a public test range; Simulate window builds a real classical oracle and plots ideal Grover probabilities.
Import targets or solved-puzzle rows
Import CSV / TSV / text reads addresses from the first column. Click a displayed P2PKH row to make it the active target. P2SH rows in this list are references only. Importing a list does not automatically launch a search against every address.
The separate solved-puzzle import requires these exact CSV headers:
bits,range_min,range_max,address,hash160_compressed,public_key,private_key
range_min, range_max and private_key are hexadecimal columns; bits is an integer. Each row’s public key, compressed hash and address are checked against its scalar. Predict page bands needs at least three suitable smaller-bit rows. Build range schedule creates metadata for intervals; it performs no candidate checks.
Automatic uses verified solved rows already loaded here when its sequence begins. The offline edition also retains its earlier prediction-comparison panel; its exported benchmark evidence is separate from the newer Anchors and Automatic reports.
11. Wormhole: coordinate index and signed search
Generate pages and look up saved coordinates
Enter a decimal page and choose Generate Page, or use Open Known Scalar. Generated records have exact scalar, coordinate, page and line information. Select a row to open it in the coordinate book, scalar page or Keybook.
Find in Saved Index accepts a full SEC key, X/Y, address or HASH160. It only examines records already saved by this browser. The coordinate index is not a precomputed index of every possible key. Its sorted index pages are different from the fixed scalar pages.
Digit constraints and page bridges
Suggest Exact Page finds the first value satisfying the 64-digit hex/wildcard mask. Its bounds are hexadecimal, and it also respects the current scalar-page floor. A mask-compatible value is not checked against an address by that action.
Calculate page bridge verifies the exact relation between two supplied page/line pairs; Reverse bridge swaps them. If both positions are known, their scalar difference is known. That identity does not provide an unknown target’s scalar.
Search a bounded public point
- Paste the full target SEC, enter the inclusive interval and its notation, then set the table-entry cap and giant-lookup budget.
- Select Plan from form to see the radius, stride and number of signed blocks.
- Choose Start / Resume. A reported collision is accepted only after a fresh scalar multiplication reproduces the target point.
- Use Pause and retain before Export checkpoint. Import the checkpoint and use Start / Resume to continue.
Changing a target or range requires a corresponding new plan. In the offline edition, reusable generator references can reduce setup work. Those cached references are not a record of target-search progress; preserve the search checkpoint separately.
12. Saving and resuming
| Work | Save | What can be restored |
|---|---|---|
| Automatic | Export report .txt or .json. Pause first for a clear checkpoint snapshot. | JSON restores the input setup for a fresh run. Only an active paused worker in the same tab can resume. |
| Pair Lab optimum scan | Export all hits (.txt). | Recorded hits can be imported into Anchors or the 3D book. This does not restore Pair Lab scan progress. |
| Anchors sampling | Pause task; Export atlas + checkpoint. | Import its JSON, then Resume paused scan. The exact next positions in the bounded windows are retained. |
| Anchors estimate / benchmark | Export estimate .txt / Export test results. | Evidence for reading and analysis; not a sampling checkpoint. |
| CPU Lab | Pause; Export checkpoint. | Import checkpoint in CPU Lab, then Resume. Its integrity and state are checked. |
| Wormhole search | Pause and retain; Export checkpoint. | Import in Wormhole and Start / Resume; reference tables may need rebuilding. |
| Saved coordinate index / offline reference cache | Stored by the browser when storage is available. | Belongs to that browser profile and site origin. It does not automatically travel with a ZIP download. |
CPU Lab and Wormhole also offer Restore tab autosave when a compatible session save exists. Keep explicit checkpoint files for work that matters; tab storage and browser storage can be cleared or unavailable.
The live site and offline address are different origins and have separate local data. Export and import the supported files when moving between them. A new software download includes the bundled samples and tools, not the work already held in your browser. Reports may include supplied scalars and WIF outputs; choose which files to share accordingly.
13. Website and offline editions
GoDaddy website: open the site's HTTPS address in a current desktop browser. No Python, PHP, database, or installation is required for visitors. Calculations and scans use your device; keep the tab open while they run.
Self-contained offline copy: download or copy the compiled index.html from the release package and open it in a current browser. Its scripts, styles, five worker engines, 3D Sphere, and manual are embedded. Browser storage and downloads can vary for local files.
Editable source edition: in the package's source folder, use Python 3 and run START_WINDOWS.bat, START_MAC_LINUX.command, or python3 start_offline.py. Open the loopback address printed by the launcher and keep it running. Stop it with Ctrl+C after exporting your work.
Export checkpoints before moving between the old site, this GoDaddy site, or a local file. Browser data belongs to the browser profile and origin; it is not copied by uploading the software. No saved personal sessions are included in this release.
14. Troubleshooting
| What you see | What to check |
|---|---|
| Inputs disagree | Remove old demo data and confirm the address, SEC, X/Y, scalar and page/line all identify the same point. Recheck decimal versus hex. |
| Known scalar outside range | Correct the bounds or remove a scalar that does not belong to this target. Bounds are inclusive. |
| Requires a full public point | An address/HASH160 is not a SEC key. Supply a known full SEC or both coordinates, or use address-compatible checks. |
| Insufficient anchor families | Import verified hits or sample the relevant range. Three independent families are needed for the heuristic; mirrored copies do not count as new families. |
| No heuristic interval / skipped interval check | Step 9 may be disabled, have insufficient data, or have returned an exact known match. Step 11 only applies to a heuristic interval. |
| No verified solved rows | Use CPU Lab’s solved CSV importer with the required headers and matching cryptographic fields before starting Automatic. |
| No match / budget reached | Read visited positions, next scalar or block, and remaining work. Continue a supported checkpoint or choose another explicit experiment; do not interpret it as elimination of the whole range. |
| Pause is taking a moment | The worker must reach its next checkpoint. Keep the tab open. Stop also cooperates with the current bounded calculation. |
| Resume unavailable after loading an Automatic report | Expected: that import restores inputs only. Run again, or use the native CPU/Anchors/Wormhole checkpoint format for its resumable search. |
| Worker will not load | Use a current browser supporting BigInt and Web Workers. On the hosted site, use HTTPS and refresh the complete compiled index.html. For the editable source edition, use the Python launcher. A host-added script policy must allow embedded scripts and blob workers. |
| Saved index appears empty | Check the browser profile, live versus offline address and local port. Storage is separate for each origin; software ZIPs do not carry browser databases. |
| Manual tab is not visible | Refresh after exporting active work. On a narrow window, scroll the tab strip horizontally. Manual is the final tab. |
15. Terms and equations
- Scalar k
- The integer used to generate a public curve point. Valid book scalars satisfy
1 ≤ k < n. - Public point Q
- The point
Q = kG. SEC is its compressed or uncompressed byte encoding. - HASH160 / address
- A hash or encoded destination used for comparison. It is different from the full public point.
- Mirror
- Point negation:
−Qhas the same X and opposite Y modulo the field prime. Its scalar isn − k. - Natural optimum anchor
- A recorded point whose compressed SEC and mirror receive natural QR masks 0 and 7 under the lab’s fixed settings.
- Anchor family
- A recorded scalar and its derived mirror treated as one independent reference family.
- Budget
- A limit on one method’s work. Its unit depends on the method: candidates, samples, trials, table entries, walk steps or lookups.
- Checkpoint versus report
- A checkpoint contains state supported by a particular resumable search. A report records what happened; Automatic report import restores setup only.
Exact page mapping
page(k) = 1 + floor((k − 1) / 1000)
line(k) = 1 + ((k − 1) mod 1000)
k = 1000 × (page − 1) + line
Exact anchor and mirror relations
A = aG
k = a + d Q = A + dG
n − k = (n − a) − d −Q = −A − dG
These equations verify navigation when the scalar or offset is known. They do not determine the unknown offset from public-key similarity or a QR pattern. Experimental predictions remain separate until an exact target comparison succeeds.
End of manual · Visual Keybook, Automatic edition · 19 September 2026
16. 3D Sphere
The 3D Sphere tab embeds the full spherical viewer inside Visual Keybook. The original Keybook, Automatic, Anchors, Pond, 4D Book, CPU Lab, Wormhole, and their controls remain available. This Manual stays the final tab.
Explore and inspect
Drag to rotate, scroll or pinch to magnify. Click a star to inspect an exact inclusive interval. Double-click a region, or choose Enter region, to subdivide it. Parent moves up one level; Whole sphere returns to the entire valid scalar range. At 1,000 keys or fewer, each point is an individual scalar. Optical magnification does not change the represented interval.
Move between the views
Show current Keybook key sends the last successfully derived Keybook scalar to its exact page in the sphere. Follow key from whole sphere highlights its containing interval at the widest scale; enter the highlighted region repeatedly to reach the individual key. Open selection in Keybook rederives the selected individual scalar in the original QR/mirror laboratory. This button is disabled for ranges; it never substitutes a range midpoint or starts a search. The Keybook tab also has a View in 3D Sphere button, which first validates and derives its input.
Inspector, list, pins, and sessions
The sphere retains its own Inspector, Book, Pins, and Manual panels. Inspector includes decimal/hex/binary scalar, page and line, curve coordinates, public-key encodings, WIFs, address forms, scripts, and mirror partner. Book is an accessible clickable list of the visible ranges or keys. Pins mark reference keys. Save session / Load preserve the sphere view, camera, and pins in JSON; these do not replace Automatic, CPU, or Wormhole checkpoints. Private values are recalculated on import. No balance queries are made.
Display and performance
The viewer is initialized only when its tab first opens. Switching away pauses its animation and retains its view, key, and pins. Expand sphere fills the browser viewport; choose Exit expanded view to restore the tabs. On a narrow display the Inspector appears below the sphere and scrolls independently. The original animation controls and reduced-motion preference remain available.
Exactness and privacy
Large scalars pass between views as decimal strings and BigInt, never floating-point numbers. Page = (k−1)//1000+1 and line = (k−1)%1000+1. Star positions are a navigation layout, not a map of nearby addresses or a predictor of unknown keys. Neither opening this tab nor moving a key starts a scan. All bridge messages remain between this page and its embedded viewer. Do not enter funded wallet secrets; scalar/page/line and saved sessions are private-key material.