504 papers. Thirteen bills.
No public handle.

Bills are the closure mechanisms a factoring claim must clear. Every paper maps to one or more bills, a disqualifying meta-cost, an escape gate, or irrelevance to the threat model.

The 13 bills, six meta-costs, and three escape gates define the current closure framework for the surveyed corpus. Bills 6, 7, and 8 remain empty in that corpus under the stated criteria, which supports the originality claim without making it absolute.

Bill activity heatmap

Number of triggers across 504 papers (some trigger multiple bills; total = 196 across 168 known-bill papers).

The estimated physical-qubit count required to factor RSA-2048 has dropped three orders of magnitude in seven years — yet the NIST 2030 / 2035 deprecation timeline remains unchanged and no government has signaled classified factoring progress.

Each finding is converted into a checkable falsifier (§04). The strongest findings concern unbroken bounds and historic-first negatives.

1. $L_N(1/3) = 1.923$ NFS heuristic constant unbroken since 1993. No paper in the corpus improves the unconditional NFS constant.
2. Boneh–Durfee $N^{0.292}$ small-$d$ bound 25 years unimproved. All 2024–2026 work parameterizes additional structure; the unconditional bound stands.
3. Deterministic factoring exponent $N^{1/5}$ unbroken unconditionally. The rank-3 lattice / second-LLL-vector result improves the log-factor only.
4. RSA-250 829-bit balanced ceiling 6+ years unbroken (Feb 2020 → May 2026). RSA-260, RSA-270, RSA-1024, RSA-2048 remain unfactored.
5. ECM record stands at 83 digits — tied October 2024 by yoyo@home/Moor with $2^{2246}+1$. Record height unchanged since 2013.
6. Bills 6, 7, 8 are empty across 504 papers — central empirical contribution.
7. No LLM has factored a balanced semiprime above ~40 digits without external tools. Adi Shamir at RSAC 2026: "There's not been any cryptographic success made by AI."
8. No novel-attack patents 2024–2026. Exhaustive USPTO/WIPO/EPO/JPO/KIPO/CIPA sweep returns zero. State actors do not patent; the absence is the signal.
9. ASIACRYPT 2024 + 2025 published zero RSA cryptanalysis papers. Across 270 papers in 17 LNCS volumes — historic first, to our knowledge.
10. Math. Comp. clean of factoring 2024–2026. Hittmeir migrated to Ramanujan Journal. Last factoring algorithm paper: Harvey–Hittmeir, June 2021.
11. 30+ senior cryptographers silent on RSA factoring. Including Rivest (R in RSA — only election security), Coppersmith (Bill 4 namesake — IDA/CCR classified pattern), Shamir (S in RSA — pivoted to neural-network cryptanalysis).
12. Government posture is reactive, not leading. CISA's January 2026 PQC product-category guidance sharpened procurement pressure, while the public transition timeline still tracks the NIST 2030/2035 frame. Aaronson's classified-resource-estimates prediction has not materialized.
13. 17 of 20 exotic-math categories produced zero factoring claims. Category theory, HoTT, model theory, ergodic, Floer/TQFT, K-theory, noncommutative geometry, SUSY QM, Yang–Mills, Langlands, motives/sheaves, mock modular forms, quantum walks, tropical geometry, derived categories, non-archimedean dynamics, Riemannian geometry — all empty.

Each negative finding is converted into a checkable trigger condition. The five highest-probability falsifiers (Live Alerts) are F2, F4, F5, F9, F11 — all in the "medium" probability band.

We commit to public update of the atlas within 7 days of any verified Bill 6 / 7 / 8 trigger. Submission of a paper triggering these bills is invited as a falsification challenge.

Each entry has a calibrated probability, an impact, and a re-poll cadence. The seven Tier 1 entries are monitored monthly.

Tier 1 monthly

Tier 2 quarterly

14 entries: Pascadi smoothness $x^{66/107}$, Mulder squareful sub-L[1/2], Tao–Sutherland–Conway factorial decomposition, Universal Shor circuit (eprint:2025/869), Priestley–Wallden QAOA-CVP 5th-order quantum advantage, Joux indefinite-form LLL, Biasse–Song quantum S-units, Babbush–Boneh ECDLP, Yoked Surface Codes, Engelberts 3-tuple lattice sieving, Vandaele Shor depth $O(n^3) \to O(n^2 \log^2 n)$, Maurya–Tannu QEC sync 2.4–3.4× LER reduction, SWIPER speculative window decoding, qt-Pegasis class-group action, Chen Drinfeld volcano (function-field bill 12 analog).

Tier 3 triggered

12 entries: Heninger–Lau–Shea exponent transforms, Pelofske batch GCD, Magic State Cultivation (Gidney–Shutty–Jones), Ekerå–Gärtner Regev-DLP, Chevignard–Fouque–Schrottenloher, Jacobi factoring circuit, Bäumer SSH-Client-Signatures Zenodo, SandboxAQ 20M-key 2025 sweep, Cunningham SNFS-336 batch 2026, p83 ECM tie 2024 (yoyo@home/Moor), RSA-150 Buhrow benchmark, ANTS-XVII Groningen accepted-papers list (publishing mid-May 2026 — calendar-driven highest probability).

38 senior cryptographers tracked 2024–2026. The original RSA architects have collectively withdrawn from factoring discourse. The single Tier-A active group is Heninger UCSD; the Caramba team won the 2025 Levchin Prize for CADO-NFS but pivoted away from RSA records.

Every empirical claim on this page resolves to public data. Run the classifier, regenerate the heatmap, audit the corpus, file a falsification.

Locked v1.16 (May 2026) — 504 papers; Bills 6/7/8 ★ empty across the corpus.