{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LKM5OXNUVFXP76ZZWDVUOOGQ7N","short_pith_number":"pith:LKM5OXNU","canonical_record":{"source":{"id":"2310.10058","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T04:48:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ae48d1f508f6f13437473dad1d2ca25e97e4b9a254f739faabf1da401e5cf347","abstract_canon_sha256":"db633d157963320f946bafad7e03249be179f72ef7f329b5323e12118fa94256"},"schema_version":"1.0"},"canonical_sha256":"5a99d75db4a96efffb39b0eb4738d0fb6640ca33f10ac1729ee52f091ac37f2b","source":{"kind":"arxiv","id":"2310.10058","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.10058","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"2310.10058v2","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.10058","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"LKM5OXNUVFXP","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_16","alias_value":"LKM5OXNUVFXP76ZZ","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_8","alias_value":"LKM5OXNU","created_at":"2026-07-05T07:29:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LKM5OXNUVFXP76ZZWDVUOOGQ7N","target":"record","payload":{"canonical_record":{"source":{"id":"2310.10058","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T04:48:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ae48d1f508f6f13437473dad1d2ca25e97e4b9a254f739faabf1da401e5cf347","abstract_canon_sha256":"db633d157963320f946bafad7e03249be179f72ef7f329b5323e12118fa94256"},"schema_version":"1.0"},"canonical_sha256":"5a99d75db4a96efffb39b0eb4738d0fb6640ca33f10ac1729ee52f091ac37f2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:29:28.915164Z","signature_b64":"A+qEGFg1bO+Ethn/D/db99H2sEwPNpMB/wSJFXD6A5hb1BN/ukvP+iozD8uDHKMj6i67QXw/KMgaZHM+a830BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a99d75db4a96efffb39b0eb4738d0fb6640ca33f10ac1729ee52f091ac37f2b","last_reissued_at":"2026-07-05T07:29:28.914634Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:29:28.914634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.10058","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":"2026-07-05T07:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AEKZ6QJHJbywTZChvsYSevL95PVluhZVH6Az34q5fUSqLItXca4zk8QM5c7AZDGzp2EDMsLismtiAXfw+ka8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:39:37.766736Z"},"content_sha256":"24421a2876ffe2ec536f23330ff2c8bc8ad4a2325029a0ac39e4209430f72bb4","schema_version":"1.0","event_id":"sha256:24421a2876ffe2ec536f23330ff2c8bc8ad4a2325029a0ac39e4209430f72bb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LKM5OXNUVFXP76ZZWDVUOOGQ7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lattice model with Fibonacci degree of degeneracy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Athena Wang","submitted_at":"2023-10-16T04:48:43Z","abstract_excerpt":"In this paper, we explore two different methods of finding the degrees of degeneracy for lattice model systems, specifically constructing one with a Fibonacci degree of degeneracy. We also calculate the number of ground states per site as the golden ratio $(\\phi)$ for the system that we constructed and extend our results to systems with $k-$Step Fibonacci degrees of degeneracy. Finally, I end with a few open questions that we may examine for future works."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.10058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.10058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7mVBsKpJDe1hVxU2a26MH0itFpVQ3KPaszl9+ZuFMD82jhRJThCA5xJ60UGZ2k/CAVGjX73pHhdWcFp6/wsFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:39:37.767317Z"},"content_sha256":"cd83638a746e4903c0a2fdea4f8d9d9d092320ba212dbf93786938bbc3dbb78a","schema_version":"1.0","event_id":"sha256:cd83638a746e4903c0a2fdea4f8d9d9d092320ba212dbf93786938bbc3dbb78a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/bundle.json","state_url":"https://pith.science/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/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":"2026-08-09T17:39:37Z","links":{"resolver":"https://pith.science/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N","bundle":"https://pith.science/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/bundle.json","state":"https://pith.science/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKM5OXNUVFXP76ZZWDVUOOGQ7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LKM5OXNUVFXP76ZZWDVUOOGQ7N","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":"db633d157963320f946bafad7e03249be179f72ef7f329b5323e12118fa94256","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T04:48:43Z","title_canon_sha256":"ae48d1f508f6f13437473dad1d2ca25e97e4b9a254f739faabf1da401e5cf347"},"schema_version":"1.0","source":{"id":"2310.10058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.10058","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"2310.10058v2","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.10058","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"LKM5OXNUVFXP","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_16","alias_value":"LKM5OXNUVFXP76ZZ","created_at":"2026-07-05T07:29:28Z"},{"alias_kind":"pith_short_8","alias_value":"LKM5OXNU","created_at":"2026-07-05T07:29:28Z"}],"graph_snapshots":[{"event_id":"sha256:cd83638a746e4903c0a2fdea4f8d9d9d092320ba212dbf93786938bbc3dbb78a","target":"graph","created_at":"2026-07-05T07:29:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.10058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we explore two different methods of finding the degrees of degeneracy for lattice model systems, specifically constructing one with a Fibonacci degree of degeneracy. We also calculate the number of ground states per site as the golden ratio $(\\phi)$ for the system that we constructed and extend our results to systems with $k-$Step Fibonacci degrees of degeneracy. Finally, I end with a few open questions that we may examine for future works.","authors_text":"Athena Wang","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T04:48:43Z","title":"A lattice model with Fibonacci degree of degeneracy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.10058","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":"sha256:24421a2876ffe2ec536f23330ff2c8bc8ad4a2325029a0ac39e4209430f72bb4","target":"record","created_at":"2026-07-05T07:29:28Z","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":"db633d157963320f946bafad7e03249be179f72ef7f329b5323e12118fa94256","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T04:48:43Z","title_canon_sha256":"ae48d1f508f6f13437473dad1d2ca25e97e4b9a254f739faabf1da401e5cf347"},"schema_version":"1.0","source":{"id":"2310.10058","kind":"arxiv","version":2}},"canonical_sha256":"5a99d75db4a96efffb39b0eb4738d0fb6640ca33f10ac1729ee52f091ac37f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a99d75db4a96efffb39b0eb4738d0fb6640ca33f10ac1729ee52f091ac37f2b","first_computed_at":"2026-07-05T07:29:28.914634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:29:28.914634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A+qEGFg1bO+Ethn/D/db99H2sEwPNpMB/wSJFXD6A5hb1BN/ukvP+iozD8uDHKMj6i67QXw/KMgaZHM+a830BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:29:28.915164Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.10058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24421a2876ffe2ec536f23330ff2c8bc8ad4a2325029a0ac39e4209430f72bb4","sha256:cd83638a746e4903c0a2fdea4f8d9d9d092320ba212dbf93786938bbc3dbb78a"],"state_sha256":"fe3b312698857c14a16d035b0bf748d590b297ec02dfcafcc3077bb5e0e92f81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qwoPVoiFXh/iacy3tFZNSmLjCEGvEPj+EGYpu78wCnLMj/KRd3QPbQWE+afIPBKMQE4uA8wAebqclRnrkSTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:39:37.772833Z","bundle_sha256":"65eae02a8f2a0b2d2fe549432b14bebbb06089a91f363c1e7f41093ab00bbf66"}}