{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OSTC3EPTKE7HMUVQOQEIIYGVTT","short_pith_number":"pith:OSTC3EPT","canonical_record":{"source":{"id":"0910.2907","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T15:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"b6221696d6ee24819379099d9b4ec24dc35787ee2b25d74fcf2ca002d0553863","abstract_canon_sha256":"9ceeb594fa6d9308da1cecd065035ec453a7af27d5165f0bd8520164067cdde7"},"schema_version":"1.0"},"canonical_sha256":"74a62d91f3513e7652b074088460d59cf0d5be8040bb34c143c1399a46adb542","source":{"kind":"arxiv","id":"0910.2907","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2907","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2907v4","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2907","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"OSTC3EPTKE7H","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OSTC3EPTKE7HMUVQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OSTC3EPT","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OSTC3EPTKE7HMUVQOQEIIYGVTT","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2907","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T15:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"b6221696d6ee24819379099d9b4ec24dc35787ee2b25d74fcf2ca002d0553863","abstract_canon_sha256":"9ceeb594fa6d9308da1cecd065035ec453a7af27d5165f0bd8520164067cdde7"},"schema_version":"1.0"},"canonical_sha256":"74a62d91f3513e7652b074088460d59cf0d5be8040bb34c143c1399a46adb542","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.973360Z","signature_b64":"y9TAc61QjMOTuOGW7FszoaBF/7W+EqOMsSn9qviMlXy9+unpy5x54uupySM+ApFKNrz2nG+JPgaco+eWkpS6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74a62d91f3513e7652b074088460d59cf0d5be8040bb34c143c1399a46adb542","last_reissued_at":"2026-05-18T01:30:15.972781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.972781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2907","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"638CQEcpOvhdY6W2RuwZiSJU1VC+7ai5OuSSGcuJLuqUX61QYb4JEEAT+4Hz1Je9wwn9kU7gKSTVC6fV2Z0kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:07:02.435814Z"},"content_sha256":"cf67aa051ffd02fdf84ffd4f9ef3fb85bc671914593ff883106bdb5d161efe2f","schema_version":"1.0","event_id":"sha256:cf67aa051ffd02fdf84ffd4f9ef3fb85bc671914593ff883106bdb5d161efe2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OSTC3EPTKE7HMUVQOQEIIYGVTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-regularity of the $p$-adic valuation of the Fibonacci sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric Rowland, Luis A. Medina","submitted_at":"2009-10-15T15:37:58Z","abstract_excerpt":"We show that the $p$-adic valuation of the sequence of Fibonacci numbers is a $p$-regular sequence for every prime $p$. For $p \\neq 2, 5$, we determine that the rank of this sequence is $\\alpha(p) + 1$, where $\\alpha(m)$ is the restricted period length of the Fibonacci sequence modulo $m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2907","kind":"arxiv","version":4},"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":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvX1V61chwTpHz/7nSM2aplx6PY6mOjBdRersDoaUBPzmze8JNecL0MgjQ3rSgoxoYOyi5rfMvg2J0jZVrEbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:07:02.436158Z"},"content_sha256":"7d4b4ba9946315f60e14f952ac307d472a556ef5291b54eb137a3e713b8e3b1c","schema_version":"1.0","event_id":"sha256:7d4b4ba9946315f60e14f952ac307d472a556ef5291b54eb137a3e713b8e3b1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/bundle.json","state_url":"https://pith.science/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/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":"2026-06-03T14:07:02Z","links":{"resolver":"https://pith.science/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT","bundle":"https://pith.science/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/bundle.json","state":"https://pith.science/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSTC3EPTKE7HMUVQOQEIIYGVTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OSTC3EPTKE7HMUVQOQEIIYGVTT","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":"9ceeb594fa6d9308da1cecd065035ec453a7af27d5165f0bd8520164067cdde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T15:37:58Z","title_canon_sha256":"b6221696d6ee24819379099d9b4ec24dc35787ee2b25d74fcf2ca002d0553863"},"schema_version":"1.0","source":{"id":"0910.2907","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2907","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2907v4","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2907","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"OSTC3EPTKE7H","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OSTC3EPTKE7HMUVQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OSTC3EPT","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:7d4b4ba9946315f60e14f952ac307d472a556ef5291b54eb137a3e713b8e3b1c","target":"graph","created_at":"2026-05-18T01:30:15Z","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 show that the $p$-adic valuation of the sequence of Fibonacci numbers is a $p$-regular sequence for every prime $p$. For $p \\neq 2, 5$, we determine that the rank of this sequence is $\\alpha(p) + 1$, where $\\alpha(m)$ is the restricted period length of the Fibonacci sequence modulo $m$.","authors_text":"Eric Rowland, Luis A. Medina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T15:37:58Z","title":"$p$-regularity of the $p$-adic valuation of the Fibonacci sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2907","kind":"arxiv","version":4},"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:cf67aa051ffd02fdf84ffd4f9ef3fb85bc671914593ff883106bdb5d161efe2f","target":"record","created_at":"2026-05-18T01:30:15Z","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":"9ceeb594fa6d9308da1cecd065035ec453a7af27d5165f0bd8520164067cdde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-15T15:37:58Z","title_canon_sha256":"b6221696d6ee24819379099d9b4ec24dc35787ee2b25d74fcf2ca002d0553863"},"schema_version":"1.0","source":{"id":"0910.2907","kind":"arxiv","version":4}},"canonical_sha256":"74a62d91f3513e7652b074088460d59cf0d5be8040bb34c143c1399a46adb542","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74a62d91f3513e7652b074088460d59cf0d5be8040bb34c143c1399a46adb542","first_computed_at":"2026-05-18T01:30:15.972781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.972781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y9TAc61QjMOTuOGW7FszoaBF/7W+EqOMsSn9qviMlXy9+unpy5x54uupySM+ApFKNrz2nG+JPgaco+eWkpS6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.973360Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2907","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf67aa051ffd02fdf84ffd4f9ef3fb85bc671914593ff883106bdb5d161efe2f","sha256:7d4b4ba9946315f60e14f952ac307d472a556ef5291b54eb137a3e713b8e3b1c"],"state_sha256":"a5a386406d6b94e7f8fd30f5c36253b596614746ac5296233aa0a0f72c10b69e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ALkbQP05afkFDnWWJl+eEylgvMyJ9CibR5yCZEve5zhPESJfYOdQzdoe8Ccy0+AQVcWRQ711460qg0RfAC2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:07:02.438351Z","bundle_sha256":"2144574b1ee3b09b810cc79985824618730382c0bd8adfbfafa620d78a98d0a2"}}