{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UANSBTFDEM2HY3PWAJKNOM2JIN","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":"633923c6cf469d71fd3c09a85423e7c0cea5a02c017a4351627a442194075d59","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-02-13T18:48:01Z","title_canon_sha256":"6f859d7f39fb99176c3c17cc9e030904c90e3433c29175684236cf4c60dfb970"},"schema_version":"1.0","source":{"id":"2602.13183","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.13183","created_at":"2026-07-15T01:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"2602.13183v3","created_at":"2026-07-15T01:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.13183","created_at":"2026-07-15T01:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"UANSBTFDEM2H","created_at":"2026-07-15T01:21:50Z"},{"alias_kind":"pith_short_16","alias_value":"UANSBTFDEM2HY3PW","created_at":"2026-07-15T01:21:50Z"},{"alias_kind":"pith_short_8","alias_value":"UANSBTFD","created_at":"2026-07-15T01:21:50Z"}],"graph_snapshots":[{"event_id":"sha256:d869da36b42e77135ef1da88c36bf034e5627baf0830ac737117d75e9485f568","target":"graph","created_at":"2026-07-15T01:21:50Z","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/2602.13183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider systems of particles on a line in which colliding particles annihilate each other and vanish. Computing exact annihilation probabilities is difficult because every collision reduces the particle count, while determinantal methods require a fixed count throughout. The ghost particle method, introduced in a companion paper for coalescence, removes the obstacle: destroyed particles continue walking as invisible ghosts, so the number of trajectories never changes. Applied to annihilation, the method yields an exact determinantal formula for the probability of any prescribed outcome - t","authors_text":"Piotr \\'Sniady","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-02-13T18:48:01Z","title":"Determinant and Pfaffian formulas for particle annihilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.13183","kind":"arxiv","version":3},"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:f553fddd155a920334088366930c74e0c990efbc91c2257ddf72c94183637c66","target":"record","created_at":"2026-07-15T01:21:50Z","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":"633923c6cf469d71fd3c09a85423e7c0cea5a02c017a4351627a442194075d59","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-02-13T18:48:01Z","title_canon_sha256":"6f859d7f39fb99176c3c17cc9e030904c90e3433c29175684236cf4c60dfb970"},"schema_version":"1.0","source":{"id":"2602.13183","kind":"arxiv","version":3}},"canonical_sha256":"a01b20cca323347c6df60254d7334943671658992b1d9fd9234e5fb99dc5da60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a01b20cca323347c6df60254d7334943671658992b1d9fd9234e5fb99dc5da60","first_computed_at":"2026-07-15T01:21:50.411913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:21:50.411913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zi6GFzYmoVb8v0vGiOMjlXmImqcuYXObF9Vn+uSGhKN72VoClrSRnXO9jAUxvuSrTsSGRu5haR0RQmVoOMmZAg==","signature_status":"signed_v1","signed_at":"2026-07-15T01:21:50.412910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.13183","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f553fddd155a920334088366930c74e0c990efbc91c2257ddf72c94183637c66","sha256:d869da36b42e77135ef1da88c36bf034e5627baf0830ac737117d75e9485f568"],"state_sha256":"0e3316a6adadbba641e0983ff3e221cba37fb7d71b7b1f2d5bdbed17f4da8df9"}