{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:ORJK7VU475NGAPD4MUMUVCEDFX","short_pith_number":"pith:ORJK7VU4","canonical_record":{"source":{"id":"math/0408263","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-08-19T14:55:16Z","cross_cats_sorted":[],"title_canon_sha256":"1e91814959a6a3fc5bb8862bd7eeef7ac9f57f148f30a5cfb81e4f4426bfe40b","abstract_canon_sha256":"e00debd365661ef48ff4aee5daf3c573fff891c1dfbaf9ed1b3fc6b779474d32"},"schema_version":"1.0"},"canonical_sha256":"7452afd69cff5a603c7c65194a88832deebdeff9d4b349a076e03ce7109d7484","source":{"kind":"arxiv","id":"math/0408263","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408263","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408263v1","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408263","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"ORJK7VU475NG","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"ORJK7VU475NGAPD4","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"ORJK7VU4","created_at":"2026-07-04T14:39:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:ORJK7VU475NGAPD4MUMUVCEDFX","target":"record","payload":{"canonical_record":{"source":{"id":"math/0408263","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-08-19T14:55:16Z","cross_cats_sorted":[],"title_canon_sha256":"1e91814959a6a3fc5bb8862bd7eeef7ac9f57f148f30a5cfb81e4f4426bfe40b","abstract_canon_sha256":"e00debd365661ef48ff4aee5daf3c573fff891c1dfbaf9ed1b3fc6b779474d32"},"schema_version":"1.0"},"canonical_sha256":"7452afd69cff5a603c7c65194a88832deebdeff9d4b349a076e03ce7109d7484","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:00.514955Z","signature_b64":"JsK527BOCI7y1HqJduqUs1XvfQQIpPwjp7xYEEPkH9X5kuA/CBxADmolJnkPV+zVQK6zfsrgS41MIxY1EZzfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7452afd69cff5a603c7c65194a88832deebdeff9d4b349a076e03ce7109d7484","last_reissued_at":"2026-07-04T14:39:00.514542Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:00.514542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0408263","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2hhnC+xqgF/ITwL//sqRqPJu9kdyUmBr5ln7htcNcGbo1cLnTdiHQjbTUe5ysn6Xl4NqHDymlBYPSivWZ2GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:05:33.046293Z"},"content_sha256":"2fa422388737b789f00d3869a4219d64c0ca7ac10f0f078aecdcd1f9eba12e97","schema_version":"1.0","event_id":"sha256:2fa422388737b789f00d3869a4219d64c0ca7ac10f0f078aecdcd1f9eba12e97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:ORJK7VU475NGAPD4MUMUVCEDFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Redheffer matrix of a partially ordered set","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Herbert S. Wilf","submitted_at":"2004-08-19T14:55:16Z","abstract_excerpt":"R. Redheffer described an $n\\times n$ matrix of 0's and 1's the size of whose determinant is connected to the Riemann Hypothesis. We describe the permutations that contribute to its determinant and evaluate its permanent in terms of integer factorizations. We generalize the Redheffer matrix to finite posets that have a 0 element and find the analogous results in the more general situation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408263","kind":"arxiv","version":1},"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/math/0408263/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":"2026-07-04T14:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pn0IDkUddKj3XOMTiJu0uRHp9QFwqIVuJ4N9ugQZ+VeiHEiNrwSSxpzuxHAi4KnTZCxkTibDNPzj4RWNteUvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:05:33.046681Z"},"content_sha256":"95e0382824aab6d3757336ae798fc7664ff9ee487ebb059d141e6256b5a4a2c3","schema_version":"1.0","event_id":"sha256:95e0382824aab6d3757336ae798fc7664ff9ee487ebb059d141e6256b5a4a2c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ORJK7VU475NGAPD4MUMUVCEDFX/bundle.json","state_url":"https://pith.science/pith/ORJK7VU475NGAPD4MUMUVCEDFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ORJK7VU475NGAPD4MUMUVCEDFX/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":"2026-07-05T09:05:33Z","links":{"resolver":"https://pith.science/pith/ORJK7VU475NGAPD4MUMUVCEDFX","bundle":"https://pith.science/pith/ORJK7VU475NGAPD4MUMUVCEDFX/bundle.json","state":"https://pith.science/pith/ORJK7VU475NGAPD4MUMUVCEDFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ORJK7VU475NGAPD4MUMUVCEDFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ORJK7VU475NGAPD4MUMUVCEDFX","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":"e00debd365661ef48ff4aee5daf3c573fff891c1dfbaf9ed1b3fc6b779474d32","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2004-08-19T14:55:16Z","title_canon_sha256":"1e91814959a6a3fc5bb8862bd7eeef7ac9f57f148f30a5cfb81e4f4426bfe40b"},"schema_version":"1.0","source":{"id":"math/0408263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408263","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408263v1","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408263","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"ORJK7VU475NG","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"ORJK7VU475NGAPD4","created_at":"2026-07-04T14:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"ORJK7VU4","created_at":"2026-07-04T14:39:00Z"}],"graph_snapshots":[{"event_id":"sha256:95e0382824aab6d3757336ae798fc7664ff9ee487ebb059d141e6256b5a4a2c3","target":"graph","created_at":"2026-07-04T14:39:00Z","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/0408263/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"R. Redheffer described an $n\\times n$ matrix of 0's and 1's the size of whose determinant is connected to the Riemann Hypothesis. We describe the permutations that contribute to its determinant and evaluate its permanent in terms of integer factorizations. We generalize the Redheffer matrix to finite posets that have a 0 element and find the analogous results in the more general situation.","authors_text":"Herbert S. Wilf","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2004-08-19T14:55:16Z","title":"The Redheffer matrix of a partially ordered set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408263","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":"sha256:2fa422388737b789f00d3869a4219d64c0ca7ac10f0f078aecdcd1f9eba12e97","target":"record","created_at":"2026-07-04T14:39:00Z","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":"e00debd365661ef48ff4aee5daf3c573fff891c1dfbaf9ed1b3fc6b779474d32","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2004-08-19T14:55:16Z","title_canon_sha256":"1e91814959a6a3fc5bb8862bd7eeef7ac9f57f148f30a5cfb81e4f4426bfe40b"},"schema_version":"1.0","source":{"id":"math/0408263","kind":"arxiv","version":1}},"canonical_sha256":"7452afd69cff5a603c7c65194a88832deebdeff9d4b349a076e03ce7109d7484","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7452afd69cff5a603c7c65194a88832deebdeff9d4b349a076e03ce7109d7484","first_computed_at":"2026-07-04T14:39:00.514542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:00.514542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JsK527BOCI7y1HqJduqUs1XvfQQIpPwjp7xYEEPkH9X5kuA/CBxADmolJnkPV+zVQK6zfsrgS41MIxY1EZzfDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:00.514955Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fa422388737b789f00d3869a4219d64c0ca7ac10f0f078aecdcd1f9eba12e97","sha256:95e0382824aab6d3757336ae798fc7664ff9ee487ebb059d141e6256b5a4a2c3"],"state_sha256":"b00820eb1759ae7e0fac3f766065f653aca1d40e52fef62b3f6f7862a10130bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2Vv+qTW36s9n2KRGWP7eMKQQ4V9MnqOI6V1m8bMwsBJOa2dpwKrODIU65CmSghgJ2re6Bg0rDeOUbjdWhrYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:05:33.048865Z","bundle_sha256":"89d73570da701ecb6b18024050770a8883640936e47af962fda2fbffe03a88ff"}}