Pith. sign in

Paper Citation Record · LEDGER

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

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:08af017bbc45f2259b9acfd0f99a7a109d0797b9c60dfe71d281753258777d0a

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:8758e69c23d367835afaf54b536e793e71958b0c858fbb18cd6ea45983efcaf5

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:5fec0143f79b1350698f97c98d449c5ddc6248a7d1f5a7a66abdf541f1870631

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:dfd4b9187f0c26cb4f6f3c916fbb8a2387b8cfd014769f7f07ac0cb4a3ae6324

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:95178c5efd64b1d7be6c22005e1b55b1642cfc0652626fe425d9bddfea313021

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:ff50c1065e89f3908dc483b5f2ef9e742714eee9b97d30146a8a517f0f6fe384

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:536321a4f1381e83d36774c530e2f88d9e8f6a8e5fef3eda0dc8f9c7eb065b4b

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:4950db589fb1a30ac8710492a983477095bc8cc0331386bbcea27f329a4f6808

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:cfa0627a652a14ca2c619610056aaa86496dd5507b5af02d3b0581c22746f47a

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:d04e280a51a1bda72ed545ffe3027661053d1fe936d6969ca28c0b79b0495b80

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:8732a39c5fa62a78d5ed0064206389382bbb6c3aaa1ce10756e4f5b669c5d53d

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:212f86ce8771f6fe850d13198d016b114ad768cfe3bc7137d84b2eb14ca86ca7

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:c804f0947dffba5dfbe5d5c6dc07201e99a1564d3b3824aa8cebe1e93aa49a55

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:eeeb2eb74a09588a3a904f5683c118fa73d80299797012e9db57cb710c26982a

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:a7c9922d3909beacaf45118ff77ff8f639feb9b33f3d15159dc0f7de3b12e948

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:5476f50f2546a7e14d8e2905ca65980c02cee374ce8c6fa9cb884917e198cd7b

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:0a3b2b65332075db7d446383ae81318b08ef78d86af572da8b9d8d77627fbe00

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:d686c764056130c572c1b4452c3481b8a13bd902ed59f8ba4aa939df29969c31

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:26f7717e7d348d3ed597e362a126341fa5938ff3cff6f677ebfb3dbd28615f8f

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:514bcecfe93fc9b65fc188e55bf7e7cf6e6ac23d7bb0c5c70d3b91b47bb0bc1c

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-20T22:31:10.408442Z digest=sha256:0b0794957a2a4ca2f097d957bf95a18f92a2adbeb5bca0e67ca2688ad7cba108

Pith citing papers

No inbound Pith citation observations are available.