{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LAYIYYKBK2CSLV3J3TV3GZCYDY","short_pith_number":"pith:LAYIYYKB","canonical_record":{"source":{"id":"1507.02872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-10T12:28:21Z","cross_cats_sorted":["math.MP","physics.comp-ph"],"title_canon_sha256":"70a7b0cff960eb6c170cc37bdb727ebb2dc270303e20599cde4548c0aad5a916","abstract_canon_sha256":"06ecc2115f6d0268a00eee2e42ece1135653976846d417b5b3682499b4dddcff"},"schema_version":"1.0"},"canonical_sha256":"58308c6141568525d769dcebb364581e2f3194c8c692c6008790bd5861718375","source":{"kind":"arxiv","id":"1507.02872","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02872","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02872v2","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02872","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"LAYIYYKBK2CS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAYIYYKBK2CSLV3J","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAYIYYKB","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LAYIYYKBK2CSLV3J3TV3GZCYDY","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-10T12:28:21Z","cross_cats_sorted":["math.MP","physics.comp-ph"],"title_canon_sha256":"70a7b0cff960eb6c170cc37bdb727ebb2dc270303e20599cde4548c0aad5a916","abstract_canon_sha256":"06ecc2115f6d0268a00eee2e42ece1135653976846d417b5b3682499b4dddcff"},"schema_version":"1.0"},"canonical_sha256":"58308c6141568525d769dcebb364581e2f3194c8c692c6008790bd5861718375","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:43.393233Z","signature_b64":"9aUMMkl50FOqpQMzuZUKXWfO2FCc7kADfCQWL4/37Ef5DEZbWFMH3M4pOjQh046zqNzs3Qsmp2l/OFanquT+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58308c6141568525d769dcebb364581e2f3194c8c692c6008790bd5861718375","last_reissued_at":"2026-05-18T01:32:43.392862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:43.392862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02872","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8G1wU1N6ZKAaIu/TI+W5IpenIJQ6FVBN50fgZdUI6az/yUzmET3iUnNCWVFD87zRA9UAvyhEQrj+wxO1PrbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:16.068255Z"},"content_sha256":"7a7bfc459909fb448fbb3e91ab21a3a9976b06234044052d1770c5926ca1f684","schema_version":"1.0","event_id":"sha256:7a7bfc459909fb448fbb3e91ab21a3a9976b06234044052d1770c5926ca1f684"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LAYIYYKBK2CSLV3J3TV3GZCYDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automata and the susceptibility of the square lattice Ising model modulo powers of primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.comp-ph"],"primary_cat":"math-ph","authors_text":"A. J. Guttmann, J-M. Maillard","submitted_at":"2015-07-10T12:28:21Z","abstract_excerpt":"We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2^r, one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2^r, and, consequently, satisfy exact functional equations modulo 2^r. We sketch a possible physical interpretation of these functional equations mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02872","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f1Sig0/7OgnxI8M15+k6IHJYjbu/Ww+gbmda5VO5sB4Yz4kxI79hgE+YMjQRZK2NwVwuxSFI3ou+icpWnEabBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:16.068949Z"},"content_sha256":"90732dc37d63f59f4c7189cb17b4b428aeec83f65fff4e7ddaf314c34db630cd","schema_version":"1.0","event_id":"sha256:90732dc37d63f59f4c7189cb17b4b428aeec83f65fff4e7ddaf314c34db630cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/bundle.json","state_url":"https://pith.science/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T18:29:16Z","links":{"resolver":"https://pith.science/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY","bundle":"https://pith.science/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/bundle.json","state":"https://pith.science/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAYIYYKBK2CSLV3J3TV3GZCYDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LAYIYYKBK2CSLV3J3TV3GZCYDY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"06ecc2115f6d0268a00eee2e42ece1135653976846d417b5b3682499b4dddcff","cross_cats_sorted":["math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-10T12:28:21Z","title_canon_sha256":"70a7b0cff960eb6c170cc37bdb727ebb2dc270303e20599cde4548c0aad5a916"},"schema_version":"1.0","source":{"id":"1507.02872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02872","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02872v2","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02872","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"LAYIYYKBK2CS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAYIYYKBK2CSLV3J","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAYIYYKB","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:90732dc37d63f59f4c7189cb17b4b428aeec83f65fff4e7ddaf314c34db630cd","target":"graph","created_at":"2026-05-18T01:32:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2^r, one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2^r, and, consequently, satisfy exact functional equations modulo 2^r. We sketch a possible physical interpretation of these functional equations mo","authors_text":"A. J. Guttmann, J-M. Maillard","cross_cats":["math.MP","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-10T12:28:21Z","title":"Automata and the susceptibility of the square lattice Ising model modulo powers of primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02872","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7a7bfc459909fb448fbb3e91ab21a3a9976b06234044052d1770c5926ca1f684","target":"record","created_at":"2026-05-18T01:32:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"06ecc2115f6d0268a00eee2e42ece1135653976846d417b5b3682499b4dddcff","cross_cats_sorted":["math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-10T12:28:21Z","title_canon_sha256":"70a7b0cff960eb6c170cc37bdb727ebb2dc270303e20599cde4548c0aad5a916"},"schema_version":"1.0","source":{"id":"1507.02872","kind":"arxiv","version":2}},"canonical_sha256":"58308c6141568525d769dcebb364581e2f3194c8c692c6008790bd5861718375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58308c6141568525d769dcebb364581e2f3194c8c692c6008790bd5861718375","first_computed_at":"2026-05-18T01:32:43.392862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:43.392862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9aUMMkl50FOqpQMzuZUKXWfO2FCc7kADfCQWL4/37Ef5DEZbWFMH3M4pOjQh046zqNzs3Qsmp2l/OFanquT+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:43.393233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a7bfc459909fb448fbb3e91ab21a3a9976b06234044052d1770c5926ca1f684","sha256:90732dc37d63f59f4c7189cb17b4b428aeec83f65fff4e7ddaf314c34db630cd"],"state_sha256":"14fb0f34b8932e9085cab32a0e22a5907da3ce45486645bffe3319b99d52c90a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EytsmUe6Xcs0Gr2DBysrGUP5htokx9v6FflfkFj/WSnZBWITynST//Ysh3sfKeGyd0uwR4EjuVAwi6WK2YerCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:29:16.072538Z","bundle_sha256":"796c3195b3d13e6b657c05681d1938ccda107c8093e3f1752a83780321e61211"}}