{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:LHUBAFHPSP5YZQ4IRCI4RFG6IB","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":"78642495c382d7352887027f859f014058dd2c0439f5508ea9a2b94928c417e7","cross_cats_sorted":["math.AG","math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2007-01-02T21:32:42Z","title_canon_sha256":"a4acc184a5faeba1cdd903652a55a57456e1036e8238db7af8935db37c1b757f"},"schema_version":"1.0","source":{"id":"math/0701075","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701075","created_at":"2026-07-04T15:02:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701075v4","created_at":"2026-07-04T15:02:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701075","created_at":"2026-07-04T15:02:37Z"},{"alias_kind":"pith_short_12","alias_value":"LHUBAFHPSP5Y","created_at":"2026-07-04T15:02:37Z"},{"alias_kind":"pith_short_16","alias_value":"LHUBAFHPSP5YZQ4I","created_at":"2026-07-04T15:02:37Z"},{"alias_kind":"pith_short_8","alias_value":"LHUBAFHP","created_at":"2026-07-04T15:02:37Z"}],"graph_snapshots":[{"event_id":"sha256:ed325638ade2ccb052402535dc57aec2ba89f3bc3d1b1983bcc2f3273da2e47f","target":"graph","created_at":"2026-07-04T15:02:37Z","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/math/0701075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and tropical geometry.","authors_text":"Matthew Baker","cross_cats":["math.AG","math.CO"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-01-02T21:32:42Z","title":"Specialization of linear systems from curves to graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701075","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":"sha256:646fa8d713674b6b65c30ac03fe28e2ea9a9c05c8b23820b7b99ea586169a33d","target":"record","created_at":"2026-07-04T15:02:37Z","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":"78642495c382d7352887027f859f014058dd2c0439f5508ea9a2b94928c417e7","cross_cats_sorted":["math.AG","math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2007-01-02T21:32:42Z","title_canon_sha256":"a4acc184a5faeba1cdd903652a55a57456e1036e8238db7af8935db37c1b757f"},"schema_version":"1.0","source":{"id":"math/0701075","kind":"arxiv","version":4}},"canonical_sha256":"59e81014ef93fb8cc3888891c894de4048dc4cb06741fe2cbb2f3f04ef9f64d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e81014ef93fb8cc3888891c894de4048dc4cb06741fe2cbb2f3f04ef9f64d8","first_computed_at":"2026-07-04T15:02:37.599125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:37.599125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qXOlD5KrPrcV+4eAHxGw8N+IFhs+y68W284YF+42Xk+/7j4vDPWZPEnGQdI7j3f28hO+OxSH3XnLXLoFbfMMDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:37.599535Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701075","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:646fa8d713674b6b65c30ac03fe28e2ea9a9c05c8b23820b7b99ea586169a33d","sha256:ed325638ade2ccb052402535dc57aec2ba89f3bc3d1b1983bcc2f3273da2e47f"],"state_sha256":"77dad958d6c4d1bcc63fdddb4e072c15dd2bc9488c4d5339a33d7c57c85a8ee8"}