{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:A2IGHV66FB5DX44EZX4UG63OWK","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":"118ea821e521766a45c9577973fa3c1bb1a9cb093c7e9a5e70350a088275d3f2","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-09-14T13:01:47Z","title_canon_sha256":"00d376c4f7bb238e452a305999874b16ccabe4068c6960b48004ed7c60a80c5d"},"schema_version":"1.0","source":{"id":"0709.2289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.2289","created_at":"2026-07-04T15:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"0709.2289v1","created_at":"2026-07-04T15:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2289","created_at":"2026-07-04T15:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"A2IGHV66FB5D","created_at":"2026-07-04T15:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"A2IGHV66FB5DX44E","created_at":"2026-07-04T15:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"A2IGHV66","created_at":"2026-07-04T15:04:16Z"}],"graph_snapshots":[{"event_id":"sha256:8406ceeec83d5ff96981c298005ecca8964347c578bd66e1d39f340aaa7919ff","target":"graph","created_at":"2026-07-04T15:04:16Z","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/0709.2289/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let t[n] be a sequence that satisfies a first order homogeneous recurrence t[n] = Q[n]*t[n-1], where Q is a polynomial with integer coefficients. The asymptotic behavior of the p-adic valuation of t[n] is described under the assumption that all the roots of Q in Z/pZ have nonvanishing derivative.","authors_text":"L. Medina, T. Amdeberhan, Victor H. Moll","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-09-14T13:01:47Z","title":"Asymptotic valuations of sequences satisfying first order recurrences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2289","kind":"arxiv","version":1},"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:faf8e24a57c3d503745d756f3a5aa459d4a0b8acd828e5434b9bafc0c54231e4","target":"record","created_at":"2026-07-04T15:04:16Z","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":"118ea821e521766a45c9577973fa3c1bb1a9cb093c7e9a5e70350a088275d3f2","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-09-14T13:01:47Z","title_canon_sha256":"00d376c4f7bb238e452a305999874b16ccabe4068c6960b48004ed7c60a80c5d"},"schema_version":"1.0","source":{"id":"0709.2289","kind":"arxiv","version":1}},"canonical_sha256":"069063d7de287a3bf384cdf9437b6eb2a9fcd703dfe1da4e71d965ed028c82bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"069063d7de287a3bf384cdf9437b6eb2a9fcd703dfe1da4e71d965ed028c82bc","first_computed_at":"2026-07-04T15:04:16.125254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:04:16.125254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YeziG2MYfmFtx1n/kdFEG9Yb4r3hlXmlkqBaoOpIwA38ZTprK4vVtMSlk7rr1GovEm7br9BVaegdp9HewOOiAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:04:16.125664Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.2289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faf8e24a57c3d503745d756f3a5aa459d4a0b8acd828e5434b9bafc0c54231e4","sha256:8406ceeec83d5ff96981c298005ecca8964347c578bd66e1d39f340aaa7919ff"],"state_sha256":"f03b5f8cfcf0cb97b22197b7041f6044823cb7301e8ffeddfbc02f07cbf6cc6f"}