{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IHK6Y3UZOO2VOUS4VZP2BTI6ID","short_pith_number":"pith:IHK6Y3UZ","canonical_record":{"source":{"id":"1611.05572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-17T05:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"ea4624c8c2df33beaacf9d65b9ced8ca73b934231ae0a101b311d6abbb08feb1","abstract_canon_sha256":"def25825e277520b0796ecf1a501dd0092b9ba88574d78c78df50920818d2231"},"schema_version":"1.0"},"canonical_sha256":"41d5ec6e9973b557525cae5fa0cd1e40ccc81eb1841f7efc1c326b1bee03f54f","source":{"kind":"arxiv","id":"1611.05572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05572","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05572v1","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05572","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"IHK6Y3UZOO2V","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IHK6Y3UZOO2VOUS4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IHK6Y3UZ","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IHK6Y3UZOO2VOUS4VZP2BTI6ID","target":"record","payload":{"canonical_record":{"source":{"id":"1611.05572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-17T05:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"ea4624c8c2df33beaacf9d65b9ced8ca73b934231ae0a101b311d6abbb08feb1","abstract_canon_sha256":"def25825e277520b0796ecf1a501dd0092b9ba88574d78c78df50920818d2231"},"schema_version":"1.0"},"canonical_sha256":"41d5ec6e9973b557525cae5fa0cd1e40ccc81eb1841f7efc1c326b1bee03f54f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:03.228397Z","signature_b64":"a+tXljqjab5xKCbZSvx6dsbllqG7Uxzrzl3ghdPK63SPFmdJnX0k50ol5bz5qPnRcrC99F64QJ9GWNVJ9Z7QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41d5ec6e9973b557525cae5fa0cd1e40ccc81eb1841f7efc1c326b1bee03f54f","last_reissued_at":"2026-05-18T00:58:03.227903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:03.227903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.05572","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":"2026-05-18T00:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAafrBpY2qZbZrmzNQWoeN/nVU1j6KPUMii1wtwXpPADaAWnIqQSZVUq564cBvvrkNlOitRyLegib2sbY2rNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:19:06.482684Z"},"content_sha256":"6d2982bb9e1da6a72424c2695590fb12803a5a8430a816d6f30797f7c9641354","schema_version":"1.0","event_id":"sha256:6d2982bb9e1da6a72424c2695590fb12803a5a8430a816d6f30797f7c9641354"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IHK6Y3UZOO2VOUS4VZP2BTI6ID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the central role of the scale invariant Poisson processes on (0,infty)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Richard Arratia","submitted_at":"2016-11-17T05:39:18Z","abstract_excerpt":"The scale invariant Poisson processes on (0,infty) play a central but mildly disguised role in number theory, combinatorics, and genetics. They give the continuous limits which underly and unify diverse discrete structures, including the prime factorization of a uniformly chosen integer, the factorization of polynomials over finite fields, the decomposition into cycles of random permutations, the decomposition into components of random mappings, and the Ewens sampling formula. They deserve attention as one of the fundamental and central objects of probability theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05572","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":""},"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":"2026-05-18T00:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWdhfwILRTYROA5XBYbZPvCy2EzlRtl8hR4Gm9RFwHFO6b7Hmee9djsFNXgGbj+nLk8bOmxFrjAqjBY+HJLsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:19:06.483027Z"},"content_sha256":"29b67ff78708e498b0d40bceff89a1df761e11b9036243e2df02b70fd55c1423","schema_version":"1.0","event_id":"sha256:29b67ff78708e498b0d40bceff89a1df761e11b9036243e2df02b70fd55c1423"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/bundle.json","state_url":"https://pith.science/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/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":"2026-06-24T08:19:06Z","links":{"resolver":"https://pith.science/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID","bundle":"https://pith.science/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/bundle.json","state":"https://pith.science/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHK6Y3UZOO2VOUS4VZP2BTI6ID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IHK6Y3UZOO2VOUS4VZP2BTI6ID","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":"def25825e277520b0796ecf1a501dd0092b9ba88574d78c78df50920818d2231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-17T05:39:18Z","title_canon_sha256":"ea4624c8c2df33beaacf9d65b9ced8ca73b934231ae0a101b311d6abbb08feb1"},"schema_version":"1.0","source":{"id":"1611.05572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05572","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05572v1","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05572","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"IHK6Y3UZOO2V","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IHK6Y3UZOO2VOUS4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IHK6Y3UZ","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:29b67ff78708e498b0d40bceff89a1df761e11b9036243e2df02b70fd55c1423","target":"graph","created_at":"2026-05-18T00:58:03Z","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 scale invariant Poisson processes on (0,infty) play a central but mildly disguised role in number theory, combinatorics, and genetics. They give the continuous limits which underly and unify diverse discrete structures, including the prime factorization of a uniformly chosen integer, the factorization of polynomials over finite fields, the decomposition into cycles of random permutations, the decomposition into components of random mappings, and the Ewens sampling formula. They deserve attention as one of the fundamental and central objects of probability theory.","authors_text":"Richard Arratia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-17T05:39:18Z","title":"On the central role of the scale invariant Poisson processes on (0,infty)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05572","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":"sha256:6d2982bb9e1da6a72424c2695590fb12803a5a8430a816d6f30797f7c9641354","target":"record","created_at":"2026-05-18T00:58:03Z","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":"def25825e277520b0796ecf1a501dd0092b9ba88574d78c78df50920818d2231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-17T05:39:18Z","title_canon_sha256":"ea4624c8c2df33beaacf9d65b9ced8ca73b934231ae0a101b311d6abbb08feb1"},"schema_version":"1.0","source":{"id":"1611.05572","kind":"arxiv","version":1}},"canonical_sha256":"41d5ec6e9973b557525cae5fa0cd1e40ccc81eb1841f7efc1c326b1bee03f54f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41d5ec6e9973b557525cae5fa0cd1e40ccc81eb1841f7efc1c326b1bee03f54f","first_computed_at":"2026-05-18T00:58:03.227903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:03.227903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a+tXljqjab5xKCbZSvx6dsbllqG7Uxzrzl3ghdPK63SPFmdJnX0k50ol5bz5qPnRcrC99F64QJ9GWNVJ9Z7QDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:03.228397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d2982bb9e1da6a72424c2695590fb12803a5a8430a816d6f30797f7c9641354","sha256:29b67ff78708e498b0d40bceff89a1df761e11b9036243e2df02b70fd55c1423"],"state_sha256":"3b43832182aa233b272e3adf11d4d5bacedf177fafaa3f6a09f89c3fff984f9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QgWubLkO5x7scVoiyMXgIVier4wZZvfmHfLkOm63T5v8R43jH3bjtEfOAj/pwHKZuBdiFEfYNpN6Wr7AIEyDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:19:06.484961Z","bundle_sha256":"1055bedfb340dee000f1ae728b5a52d31ce1df5dd86566b7d7a9eb58a1646593"}}