Paper Citation Record · LEDGER

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

As of 11 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 4 inbound Pith citation observations for arXiv:2507.13342.

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

pith.paper-citation-record.v1
2507.13342 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:37:28.150148Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T19:24:15.545701Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T14:30:03.723760Z

Reference resolution

24 of 24 outbound references displayed

verified exact0
verified fuzzy16
unresolved7
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0856d559-daee-4cf8-8c60-81a48d6d286c · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.364230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 59b5c1b8-e46c-4f65-a6bf-37a0f3a989f8 · outbound

This paper cites Table of expander graphs referenced in this work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Table of expander graphs referenced in this work

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.356496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation da17fac5-055b-4c6b-b1c1-2d8908619067 · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.372204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8a9db239-779b-4aa7-9a84-2ee800f0365e · outbound

This paper cites However, as shown in Ref.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes However, as shown in Ref

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.348468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a36b148d-e757-4275-857b-d04fe9a748cf · outbound

This paper cites clusters.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes clusters

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.340472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 556a60e8-f4de-4b8a-a4a9-1342943633c9 · outbound

This paper cites thermodynamic limit.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes thermodynamic limit

Reference 6

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T16:37:28.332690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0ecce14-67b7-4561-bc30-fb11573f45aa · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.324558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9c369e5e-6c4f-4315-a803-8bbbfd0611d1 · outbound

This paper cites relevant.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes relevant

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.316550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dc224945-a3e5-4603-bc47-0fdc486024b5 · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.308294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fdc04e6b-e710-4906-8efe-d198d98c2f08 · outbound

This paper cites Energy density Configuration Space T typical cluster atypical cluster 0 FIG.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Energy density Configuration Space T typical cluster atypical cluster 0 FIG

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.300322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 419b319b-d448-4aa4-9a19-f76def4b29d0 · outbound

This paper cites Definition E.1.We call a binary matrixH∈F m×n 2 (w, b)-sparseif each row has Hamming weight≤wand each column has Hamming weight≤b.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Definition E.1.We call a binary matrixH∈F m×n 2 (w, b)-sparseif each row has Hamming weight≤wand each column has Hamming weight≤b

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.292108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5a7e11c9-35dd-46f2-a5ed-78df8c45567c · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.284151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 49c443b9-3d31-4bed-9b3b-8a1ecb41d802 · outbound

This paper cites symmetrized.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes symmetrized

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.276142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e1fc2043-652c-4aab-9991-7eb82209b3f2 · outbound

This paper cites symmetrized.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes symmetrized

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.267212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 47a7286c-899e-4499-9bdf-4143d4cbdbac · outbound

This paper cites redundant.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes redundant

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.258955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bbb0e9d8-a376-414c-83c3-fec8bf6088fe · outbound

This paper cites We can represent this conveniently as a tensor network (see also Refs.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes We can represent this conveniently as a tensor network (see also Refs

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.250071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f228d33d-a42b-4c05-aa86-5e4e6331ed78 · outbound

This paper cites inconsistent.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes inconsistent

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.241785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 767f5f37-3bbd-485f-9b13-00e5be885e8f · outbound

This paper cites ferromagnetic.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes ferromagnetic

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.233465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 14cd4233-292a-449e-b794-2051b45660f2 · outbound

This paper cites ForT < Tmem,h opp bulk(T)>0: up to this point, a strong enough negative boundary field can overwhelm the positive boundary field.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes ForT < Tmem,h opp bulk(T)>0: up to this point, a strong enough negative boundary field can overwhelm the positive boundary field

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.224318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0ed3ba5-2a41-408c-b40b-1f7fba2f692d · outbound

This paper cites annealed.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes annealed

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.214720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fba080cb-ba89-4126-943d-307aba16fc0a · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.206002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 84d9e48b-31f2-45d4-ad4d-9c2bb3aced19 · outbound

This paper cites an unresolved cited work.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:37:28.197555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4cf584c6-d637-4a1c-ba22-8400e2158fbf · outbound

This paper cites spin glass.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes spin glass

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.189249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5de0a876-0227-4145-a19a-cc3ae3bb22dc · outbound

This paper cites We measure the entropy density in bits, so thats= β(ε−f)/ln(2) whereε, fare the energy density and free- energy density, respectively, at a given temperature.

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes We measure the entropy density in bits, so thats= β(ε−f)/ln(2) whereε, fare the energy density and free- energy density, respectively, at a given temperature

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:37:28.180563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 60151495-4b68-46da-97e7-a3150484b8ca · inbound

Superconductivity in hyperbolic spaces: Regular hyperbolic lattices and Ginzburg-Landau theory cites this paper.

Superconductivity in hyperbolic spaces: Regular hyperbolic lattices and Ginzburg-Landau theory Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-04T19:24:15.545701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb58ae23-9592-452e-bf56-ed8143044396 · inbound

Topological states and flat bands in exactly solvable decorated Cayley trees cites this paper.

Topological states and flat bands in exactly solvable decorated Cayley trees Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T22:20:16.110943Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6782d35-ab26-4d63-8274-23280f0353ae · inbound

Coupled-Layer Construction of Quantum Product Codes cites this paper.

Coupled-Layer Construction of Quantum Product Codes Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-15T14:30:03.725627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c64883ce-3709-48e8-9e4e-2c418e84e99c · inbound

Lifting Lifted Product Codes cites this paper.

Lifting Lifted Product Codes Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

Reference 87

Resolution: unresolved; no resolver link, observed 2026-07-31T01:57:11.979636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.