{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:TTUAWDKNZURCDIUZN7SSJFBFFE","short_pith_number":"pith:TTUAWDKN","canonical_record":{"source":{"id":"0902.0709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-04T11:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"b1bfa3c48b231410cc1f6b1f54be88b0b2bb03dd4ea07424b3d6efb1b87c33f8","abstract_canon_sha256":"47b06fc18473207d67689f3877868a8de90b76e41249fc66ae816c576c89a430"},"schema_version":"1.0"},"canonical_sha256":"9ce80b0d4dcd2221a2996fe524942529359e7a4b60f68187ba521ba8efcf8047","source":{"kind":"arxiv","id":"0902.0709","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0709","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0709v2","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0709","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"TTUAWDKNZURC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"TTUAWDKNZURCDIUZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"TTUAWDKN","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:TTUAWDKNZURCDIUZN7SSJFBFFE","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-04T11:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"b1bfa3c48b231410cc1f6b1f54be88b0b2bb03dd4ea07424b3d6efb1b87c33f8","abstract_canon_sha256":"47b06fc18473207d67689f3877868a8de90b76e41249fc66ae816c576c89a430"},"schema_version":"1.0"},"canonical_sha256":"9ce80b0d4dcd2221a2996fe524942529359e7a4b60f68187ba521ba8efcf8047","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:00.786753Z","signature_b64":"tYXMS9klgrJ2Rc2HI2+pqSyWGWGVr2W+nkCeN32BvoRcdOP572pJv7hA93YFS7gBCBok/8ebhrT37ItiIwxeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ce80b0d4dcd2221a2996fe524942529359e7a4b60f68187ba521ba8efcf8047","last_reissued_at":"2026-05-18T04:40:00.786265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:00.786265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0709","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRRBbeM3HqDFAE5yQfkYfTPrEO0agfQaoUXtEejiyeVk59FhqQyFdXBYXyUFlvVfzoMQV+c3rlRPdMsm1bUXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:14:58.118510Z"},"content_sha256":"cddaf243337fb802aa9cd982e86fcee2beeb02dde69c8607c384209f1af014c8","schema_version":"1.0","event_id":"sha256:cddaf243337fb802aa9cd982e86fcee2beeb02dde69c8607c384209f1af014c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:TTUAWDKNZURCDIUZN7SSJFBFFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Finitization of the Bead Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin J. Fleming, Eric Nordenstam, Peter J. Forrester","submitted_at":"2009-02-04T11:53:25Z","abstract_excerpt":"The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an $abc$-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0709","kind":"arxiv","version":2},"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":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jUoFMo2Zz0nAKLt7p6m3DvQy0PfHoXHrl0PdFnr19uF+JAEbtiEQGwz6EKqLC8KlH63qjksEm6jv98mGzuVeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:14:58.118864Z"},"content_sha256":"4586941ec4229feee1c4be380c69f61518fa923ae82894399efa3dbff2362200","schema_version":"1.0","event_id":"sha256:4586941ec4229feee1c4be380c69f61518fa923ae82894399efa3dbff2362200"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/bundle.json","state_url":"https://pith.science/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/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":"2026-06-03T08:14:58Z","links":{"resolver":"https://pith.science/pith/TTUAWDKNZURCDIUZN7SSJFBFFE","bundle":"https://pith.science/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/bundle.json","state":"https://pith.science/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTUAWDKNZURCDIUZN7SSJFBFFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TTUAWDKNZURCDIUZN7SSJFBFFE","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":"47b06fc18473207d67689f3877868a8de90b76e41249fc66ae816c576c89a430","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-04T11:53:25Z","title_canon_sha256":"b1bfa3c48b231410cc1f6b1f54be88b0b2bb03dd4ea07424b3d6efb1b87c33f8"},"schema_version":"1.0","source":{"id":"0902.0709","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0709","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0709v2","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0709","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"TTUAWDKNZURC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"TTUAWDKNZURCDIUZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"TTUAWDKN","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:4586941ec4229feee1c4be380c69f61518fa923ae82894399efa3dbff2362200","target":"graph","created_at":"2026-05-18T04:40:00Z","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"},"paper":{"abstract_excerpt":"The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an $abc$-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of","authors_text":"Benjamin J. Fleming, Eric Nordenstam, Peter J. Forrester","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-04T11:53:25Z","title":"A Finitization of the Bead Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0709","kind":"arxiv","version":2},"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:cddaf243337fb802aa9cd982e86fcee2beeb02dde69c8607c384209f1af014c8","target":"record","created_at":"2026-05-18T04:40:00Z","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":"47b06fc18473207d67689f3877868a8de90b76e41249fc66ae816c576c89a430","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-04T11:53:25Z","title_canon_sha256":"b1bfa3c48b231410cc1f6b1f54be88b0b2bb03dd4ea07424b3d6efb1b87c33f8"},"schema_version":"1.0","source":{"id":"0902.0709","kind":"arxiv","version":2}},"canonical_sha256":"9ce80b0d4dcd2221a2996fe524942529359e7a4b60f68187ba521ba8efcf8047","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ce80b0d4dcd2221a2996fe524942529359e7a4b60f68187ba521ba8efcf8047","first_computed_at":"2026-05-18T04:40:00.786265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:00.786265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tYXMS9klgrJ2Rc2HI2+pqSyWGWGVr2W+nkCeN32BvoRcdOP572pJv7hA93YFS7gBCBok/8ebhrT37ItiIwxeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:00.786753Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0709","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cddaf243337fb802aa9cd982e86fcee2beeb02dde69c8607c384209f1af014c8","sha256:4586941ec4229feee1c4be380c69f61518fa923ae82894399efa3dbff2362200"],"state_sha256":"f60b0aee493c5b15283f20d947149f114725fb9cfbe1a4b4e0e717590c340a4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUrWTu51WVHHWKOLoKRkkN5YRT6YBGEDYb7cjYLbIqPiinJlrr/IVQRCzUm09sKku8bAcmNjNKGNds3goK/fBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:14:58.120818Z","bundle_sha256":"2ab836a5011c8e255694750162de1f65b1271885b199eff3bbfd25a1e021d077"}}