F1 syndrome-pencil normal form
PR #118 gives a Hankel-pencil incidence test for support-wise line explanations and a matching noncontainment criterion.
Research-grade certificates for smooth RS MCA
Can you push RS MCA frontier?
An interactive frontier board for Reed–Solomon mutual correlated agreement failure certificates. Track how far below capacity a smooth RS row can still certify \(\varepsilon_{\rm mca}(C,\delta)>2^{-128}\), with field ledgers, admissibility gates, and non-claims visible by default.
\[
\text{score}=128+\log_2\!\left(\frac{N_{\rm bad}}{q_{\rm line}}\right)
\]
Best certified margin+32.82bits above the 2−128 failure line
Best strict radius249/512Cycle119 strict263 proof record
Bad challenges52.7Bdistinct gamma values imported from Cycle84
Next threshold≥ 7bad slopes clear 2−128 over F1732
Frontier progress
Every point is a proof record, candidate, or target with a row, radius, field denominator, predicate, and status. Smaller reserve means closer to capacity; higher margin means more certified failure mass.
Selected certificate
Click a chart point or leaderboard row to inspect the row, radius, proof status, and non-claims.
Leaderboard
The primary score is \(128+\log_2(N_{\rm bad}/q_{\rm line})\). Positive score means the certificate exceeds the ABF target threshold.
| Entry | Radius | Slack | Bad slopes | Score | Status |
|---|---|---|---|---|---|
| Cycle116 closed-threshold proof record ABF printed closed threshold at delta = 125/256. |
125/256 | σ=6 | 52,747,567,092 | +32.82 | proof record |
| Cycle119 strict263 proof record Two-ended upgrade with one-symbol strict margin. |
249/512 | σ=7 | 52,747,567,092 | +32.82 | proof record |
| Strict264 minimal threshold target First Paper-B slack upgrade target: only seven retained slopes are enough. |
31/64 | σ=8 | 7 | +0.01 | target |
| Strict264 2187-slope candidate Candidate subpacket shape if the hinted strict264 target is validated. |
31/64 | σ=8 | 2,187 | +8.30 | candidate |
| Reserve-scale target sigma = 16 A more serious finite-slack target. |
15/32 | σ=16 | 7 | +0.01 | target |
| Reserve-scale target sigma = 32 Deeper below capacity; still only seven retained slopes are enough. |
7/16 | σ=32 | 7 | +0.01 | target |
| n/log n scale target sigma ~= 57 Closer to the local-limit reserve scale. |
199/512 | σ=57 | 7 | +0.01 | target |
Existing results
Recent proof notes, audits, counterexample families, and bridge results are pulled into a browsable result ledger with source links.
L2 interleaved codegree reduction
PR #108 proves a two-regime and recursive reduction from interleaved lists to base-code lists at agreements a and 2a-k.
Paper D MCA cap gets a CS25-free route
PR #115 isolates a simple-pole/deep-point averaging proof route for the headline MCA cap under Paper D's finite-field hypotheses.
Strict264 remains a seven-slope target
PR #110 confirms the arithmetic: over F_17^32, seven retained slopes at agreement 264 would clear 2^-128.
Large-domain mixed-Weil energy floor
PR #119 adds a possible L1 route cut for large-domain prefix-dual energy, kept conditional pending the mixed Weil citation and constant check.
Cycle119/Cycle120 ABF-row obstruction
The active value remains 52,747,567,092 bad challenges over F_17^32; Cycle116 reaches the printed closed endpoint and Cycle119 gives the strict endpoint if finite inputs check out.
Standalone Cycle120 LDsw proof note
PR #105 adds a compact standalone note for the source-scoped lower bound LD_sw(RS[F_17^32,H,256],262) >= 52,747,567,092.
Exact MCA to line-decoding normalization
PR #102 records the support-wise identity epsilon_mca(C,delta) = LD_sw(C,ceil((1-delta)n))/|F| for the two-source object.
Extension-line lower floors
PR #103 strengthens the F1 warning: fixed-rate extension-line families create floors before extension-degree dilution.
M1 beta-pushforward spectral audit
PR #104 scans beta-pushforward rows and finds no hidden growing p^2 mass in the tested windows.
L1 quotient-budgeted locator route
PRs #99 and #106 add characteristic-zero prefix reductions, bad-prime proof-record machinery, and a full-list quotient proof program.
Sharp interleaved-list target
PR #107 sharpens L2: interleaved-list analysis should charge quotient-core mass diagonally and avoid the naive Cartesian-product numerator.
X1 bridges and Lean formalization stub
PR #101 adds deep-point/interleaved bridge notes, quotient-reduction notes, prize-path maps, and a small Lean scaffold.
Certificate calculator
Check whether a proposed row clears the exact integer test \(2^{128}N_{\rm bad}>q_{\rm line}\), and see the induced radius for the fixed \([512,256]\) row.
For this fixed row, \(\delta=1-a/512\), \(\sigma=a-k\), and \(\eta=1/2-\delta=\sigma/512\).
Admissibility gates
A certificate is only useful if row, predicate, sampler, radius convention, and event-retention semantics are made explicit.
✓
RS row
Explicit \(\mathrm{RS}[F,L,k]\), rate in the challenge set, smooth domain, and degree bound.
✓
Support-wise predicate
One support \(S\) explains the combination but not the two source words on the same support.
✓
Sampler
\(\gamma\) is sampled uniformly from the line field used in the denominator.
✓
Radius convention
Closed and strict support thresholds are shown separately to prevent endpoint ambiguity.
!
Event retention
Any endpoint, duplicate, quotient, charge, or retained-event filter must print the retained numerator.
!
Non-claims
Not ordinary list decoding, not protocol soundness, not an efficient attack, not exact \(\delta_C^*\).
Why this board exists
Paper B turns no-slack smooth-domain failures into a corrected slack ledger. The frontier asks which certified bad-slope sets survive at larger agreement slack.
Slack frontier
For \(C=\mathrm{RS}[\mathbb F_{17^{32}},H,256]\), a certificate at agreement \(a=256+\sigma\) proves failure at \(\delta=1-a/512\).
Strict264
Agreement 264 means \(\sigma=8\) and \(\delta=31/64\). Since \(\lfloor17^{32}/2^{128}\rfloor=6\), seven retained slopes already beat \(2^{-128}\).
Replay before publicity
Each entry should identify whether the census was rerun, hash-bound, imported, locally checked, peer-reviewed, or only proposed.
Contributor artifacts
The board keeps claims, checkers, thresholds, audits, and failure modes next to their source notes so results can be inspected before they are reused.
Papers
The main references behind the frontier. Paper A explains the obstruction, Paper B rebuilds the reserve theory, Paper C tracks protocol ledgers, and Paper D gives the universal field-size cap.
A
Paper A
Paper A: No-Slack Obstruction
Refutes the old no-slack support-wise line-MCA statement for smooth multiplicative Reed-Solomon domains.
B
Paper B
Paper B: Slack, Quotient, and Entropy Theory
Builds the corrected-reserve theory and names the main local-limit, quotient, extension, and MCA proof targets.
C
Paper C
Paper C: SNARK and Protocol Ledger
Separates protocol soundness accounting from list, CA, MCA, line-decoding, extension, and interleaving ledgers.
D
Paper D
Paper D: Universal Field-Size Cap
Uses the Crites-Stewart list-to-agreement conversion to prove a universal MCA threshold cap in the relevant sub-capacity band.
Collaborate on GitHub
Send pull requests with narrow, reviewable proof notes, audits, scripts, certificates, or site-data updates. Keep new research material experimental first.
github.com/przchojecki/rs-mca
Open an issue for discussion or send a PR with reproducible evidence. PRs should say exactly which theorem, target, or ledger they affect.
Where to put work
1. Read AGENTS.md first
Follow the field-ledger, status-label, and no-main-paper-edit rules before proposing a result.
2. Add new research under experimental/
Use notes for theorem sketches and audits, scripts for reproducible checks, and data certificates for machine-readable outputs.
3. Update experimental/agents-log.md
Record date, contributor, files changed, status, usefulness, and the next step for anything materially changed in experimental/.
4. Touch site/data/ only for public entries
Add board rows after the source note exists and the status is explicit: proved, conditional, conjectural, experimental, audit, or counterexample.
What a PR should include
Claim and status
State the exact claim and label it PROVED, CONDITIONAL, CONJECTURAL, EXPERIMENTAL, AUDIT, or COUNTEREXAMPLE.
Parameters and ledgers
Print \(q_{\rm gen}\), \(q_{\rm line}\), \(q_{\rm chal}\), base/extension fields, \(n\), \(k\), \(\rho\), \(\delta\), \(\eta\), and the exact object being bounded.
Reproducibility
Attach a script, JSON certificate, symbolic proof note, seed, hash, or exact command that lets reviewers replay the result.
Board impact
Say whether the PR changes entropy, quotient, interleaved-list, MCA, line-decoding, field-transfer, or query-budget ledgers.