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Paper Citation Record · LEDGER

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision

As of 21 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2605.18820.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2605.18820 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-20T22:31:10.408442Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

  • verified exact3
  • verified fuzzy9
  • unresolved8
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 631a2a55-5347-42e0-92ae-6211a4a083d0 · outbound

This paper cites Birth of a Transformer: A Memory Viewpoint.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Birth of a Transformer: A Memory Viewpoint

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-05-20T22:33:48.626282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:934dc34fa15dff54ee13b999267a7cb4e9845545be4c8d821245c4a20586668b

Observation 95f07320-f12c-4e91-b456-0723a8184616 · outbound

This paper cites Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-05-20T22:33:48.630046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:c8d6ccd0d5f82485baf60b9f8d5a83df4f648929fc299548c903a18fac1a996d

Observation d39ca81d-d515-44a6-86f2-3c88c4cbedf2 · outbound

This paper cites Zhiyuan Li, Hong Liu, Denny Zhou, and Tengyu Ma.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Zhiyuan Li, Hong Liu, Denny Zhou, and Tengyu Ma

Reference 3

Resolution
verified exact
doi, observed 2026-05-20T22:33:48.090327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:ba57aedfb5f3e55c534f13ec3c0614fc9dd9c5e2267ddcc53883d89f59daaaae

Observation 597916c0-bbc9-41d8-b410-ea2bcc99e8eb · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.009976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:22bb1bde784dc1be643c9f57838e441aa404c8930933ff26c6cbb872e5a2035c

Observation 8bf23f8b-40c6-4457-bd8a-6f43a3449240 · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.068574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:0d7318e305715607e10e77e42ba3f9a2dd71bbe67089166da23d3300f3bccbb4

Observation d6d7c395-05f6-4fb4-b9ca-279bcac1a979 · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.014682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:286f8f9a394db8c307396ac210dc5b747a4b5f3296870529262a4a65811402b0

Observation d6852666-0de9-400a-a9b8-019cc9ed338a · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.046295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:858fe7a3cd744570c9c527b16ccda89bfbf381a4c290a5991713c1eaea762084

Observation 05c0c2fa-5793-4f8d-abf8-2064f643e2f9 · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.051087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:2430c5fbadeb31ec5261703a54f88e8a35c88160d81047f8aa1a7d071af30d0a

Observation 7c1ef046-3a26-4584-906f-a62044f88fd2 · outbound

This paper cites 4.m (c) f =k c+1 −k c =k c(np−1)(1+o(1)) in the tree regime, som(c) f = (np)c(np−1)(1± O( p logn/(np) c)).

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision 4.m (c) f =k c+1 −k c =k c(np−1)(1+o(1)) in the tree regime, som(c) f = (np)c(np−1)(1± O( p logn/(np) c))

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.041934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:39bce50bd8c526bd98835cda5e613bdfbc38725e1292a7866cf5d4ee1aa331d6

Observation 9dd0c3e3-0551-437e-a26c-1415d8d0a54d · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:09.995202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:4f37e851dec4ffda905cb6860270cb3ba737ae5035c68f2647836897ffc49b14

Observation 322919b8-08f5-4a31-9a7a-ca15409fad3c · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.000729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:008cf50bc2562fb95ddc12369a0fca6bebcaa57a61fef205ce05377b6a84c98d

Observation a17766bf-4a29-44f4-bec3-5e07fd60d2cc · outbound

This paper cites learnability cliff.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision learnability cliff

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.021348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:a7a02c85cf9747d0f3d8f1726d7de99c9b131f65553902f08def9b303a86c4a3

Observation 5d3a7c11-fd8b-4ceb-8df7-5ff7349c12c6 · outbound

This paper cites The two-term decomposition matches the bias-variance analysis of §6.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision The two-term decomposition matches the bias-variance analysis of §6

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.072839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:bd78f1fad2fc4106f7fc464a41b398a06e81994e811fe5093975120f583137a7

Observation 25566514-1d31-431b-94c6-89efefdf6745 · outbound

This paper cites For b′ 1 <0 (forward-invariant by Lem.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision For b′ 1 <0 (forward-invariant by Lem

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.055532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:9322e342bc039ecffde9dc119110d8fe3598e44b9b94b753837e09672ddbbcb0

Observation e04aab27-6877-41d6-85c8-9664b7f47391 · outbound

This paper cites Global Convergence.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Global Convergence

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.031305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:935f4667606cbd14d2e802e00b2ebcc0a75c40d18f5f62df2b6f560ac31d0fe9

Observation 0803c3c5-4ce2-4149-b134-19cd3606d791 · outbound

This paper cites DefiningA:= 1 +ηaandB:=ηb ′ 1, αeff,c = α A+m (c) f B A+ √kc B.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision DefiningA:= 1 +ηaandB:=ηb ′ 1, αeff,c = α A+m (c) f B A+ √kc B

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.035861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:66235e8b745bcb65c021a57184db645899337258814a9137b5025ba915b759f4

Observation 1b7b7e1c-5aac-4d24-865e-1781dd22e859 · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-05-20T22:34:10.060044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:38900ddc4521461a60f5e7319abc78fdceb8a92995604de269fe6474e3ee9ba6

Observation 36234f13-ca42-469a-b987-284e5452f2db · outbound

This paper cites an unresolved cited work.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision Unresolved cited work

Reference 18

Resolution
malformed identifier
raw_fallback, observed 2026-05-20T22:34:10.005373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:c0190476cb607fc006943dbbdcc293633affa12c61419c652f18b39ad02c0f33

Observation b204495f-7d87-4180-b6eb-281060744a26 · outbound

This paper cites This establishes adescent rate ˙V| Stage1 ≤ −κ AVat the saddle.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision This establishes adescent rate ˙V| Stage1 ≤ −κ AVat the saddle

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.064576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:bd9eec84cb2cbb6245e5faf803a564891948c211924c5234a72280bf0bec46ca

Observation 91bc4f83-45b5-411d-b5fb-1365cf788714 · outbound

This paper cites This contributes a multiplicative factorR 2 c ≥poly(D) −2 to the descent rate.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision This contributes a multiplicative factorR 2 c ≥poly(D) −2 to the descent rate

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:09.984895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:42f1202f9c681f2774b2ef39d80b3d09a23b3704ab1f01f8139f862c4a6e116f

Observation f888cc0a-71e2-4182-94fd-04f6de0c13b5 · outbound

This paper cites This contributes a final multiplicative factor Imin λ⊥ to the contraction near the Möbius variety.

Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision This contributes a final multiplicative factor Imin λ⊥ to the contraction near the Möbius variety

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-05-20T22:34:10.026976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:64aec16fbd0f8da479eb82796eaa283729fb5987f1f1adb9dac8cdc1e38f5736

Pith citing papers

No inbound Pith citation observations are available.