{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KJB2U7BCAOO73DQYFRQDPOQ5LL","short_pith_number":"pith:KJB2U7BC","canonical_record":{"source":{"id":"1603.03218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-10T10:49:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"20306b8c752fd499ec207a9be0bd8c762d25ccb614893f7975b4004591a711d6","abstract_canon_sha256":"e999eece2f77d03fd1fb813b303869e13963949eea9366a25621912c25222463"},"schema_version":"1.0"},"canonical_sha256":"5243aa7c22039dfd8e182c6037ba1d5add7a5f2b9615be3d21654a81b1b768ae","source":{"kind":"arxiv","id":"1603.03218","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03218","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03218v3","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03218","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"KJB2U7BCAOO7","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KJB2U7BCAOO73DQY","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KJB2U7BC","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KJB2U7BCAOO73DQYFRQDPOQ5LL","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-10T10:49:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"20306b8c752fd499ec207a9be0bd8c762d25ccb614893f7975b4004591a711d6","abstract_canon_sha256":"e999eece2f77d03fd1fb813b303869e13963949eea9366a25621912c25222463"},"schema_version":"1.0"},"canonical_sha256":"5243aa7c22039dfd8e182c6037ba1d5add7a5f2b9615be3d21654a81b1b768ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:12.168257Z","signature_b64":"YkW8C1GkppPL4JF4QWEpUAwvrAkPjSdHz60yMCE4vfxPmHHdytaI9bLAbOTYGOV59yKqQBryEx2DUVvUNxzLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5243aa7c22039dfd8e182c6037ba1d5add7a5f2b9615be3d21654a81b1b768ae","last_reissued_at":"2026-05-17T23:48:12.167431Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:12.167431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03218","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRJF93dGblrTQjLmJWuraanJLBzDlXOMtArnqLfC4tgv5hzHaWxXrY/ba6jsDTyYUq/g+2voNqG8WbVT4DbZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:19:29.706305Z"},"content_sha256":"bbb32565569db43afdf56d8a4abe07072e6eb8efb744b85edd23376b76f0aa85","schema_version":"1.0","event_id":"sha256:bbb32565569db43afdf56d8a4abe07072e6eb8efb744b85edd23376b76f0aa85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KJB2U7BCAOO73DQYFRQDPOQ5LL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Particle Diffusion Limited Aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexandre Stauffer, Vladas Sidoravicius","submitted_at":"2016-03-10T10:49:48Z","abstract_excerpt":"We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \\mu. In addition, there is an aggregate, which initially consists of the origin. Non-aggregated particles move as continuous time simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is referred to as multi-particle diffusion limited aggregation.\n  Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03218","kind":"arxiv","version":3},"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":"2026-05-17T23:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejudoZrL8NLKqLGin9w+DZxNsgpuoRNVYIuWLkBHksCss1lByRox51ZaTSRhSPnJj6yLMvGKRz+6U1mVJO81Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:19:29.706989Z"},"content_sha256":"0c853ffbe0d97be93c2452a01a6f4019939f18f1ba471cec7156ae2a73f1ca52","schema_version":"1.0","event_id":"sha256:0c853ffbe0d97be93c2452a01a6f4019939f18f1ba471cec7156ae2a73f1ca52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/bundle.json","state_url":"https://pith.science/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/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":"2026-05-27T22:19:29Z","links":{"resolver":"https://pith.science/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL","bundle":"https://pith.science/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/bundle.json","state":"https://pith.science/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJB2U7BCAOO73DQYFRQDPOQ5LL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KJB2U7BCAOO73DQYFRQDPOQ5LL","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":"e999eece2f77d03fd1fb813b303869e13963949eea9366a25621912c25222463","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-10T10:49:48Z","title_canon_sha256":"20306b8c752fd499ec207a9be0bd8c762d25ccb614893f7975b4004591a711d6"},"schema_version":"1.0","source":{"id":"1603.03218","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03218","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03218v3","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03218","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"KJB2U7BCAOO7","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KJB2U7BCAOO73DQY","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KJB2U7BC","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:0c853ffbe0d97be93c2452a01a6f4019939f18f1ba471cec7156ae2a73f1ca52","target":"graph","created_at":"2026-05-17T23:48:12Z","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":"We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \\mu. In addition, there is an aggregate, which initially consists of the origin. Non-aggregated particles move as continuous time simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is referred to as multi-particle diffusion limited aggregation.\n  Our","authors_text":"Alexandre Stauffer, Vladas Sidoravicius","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-10T10:49:48Z","title":"Multi-Particle Diffusion Limited Aggregation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03218","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:bbb32565569db43afdf56d8a4abe07072e6eb8efb744b85edd23376b76f0aa85","target":"record","created_at":"2026-05-17T23:48:12Z","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":"e999eece2f77d03fd1fb813b303869e13963949eea9366a25621912c25222463","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-10T10:49:48Z","title_canon_sha256":"20306b8c752fd499ec207a9be0bd8c762d25ccb614893f7975b4004591a711d6"},"schema_version":"1.0","source":{"id":"1603.03218","kind":"arxiv","version":3}},"canonical_sha256":"5243aa7c22039dfd8e182c6037ba1d5add7a5f2b9615be3d21654a81b1b768ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5243aa7c22039dfd8e182c6037ba1d5add7a5f2b9615be3d21654a81b1b768ae","first_computed_at":"2026-05-17T23:48:12.167431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:12.167431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YkW8C1GkppPL4JF4QWEpUAwvrAkPjSdHz60yMCE4vfxPmHHdytaI9bLAbOTYGOV59yKqQBryEx2DUVvUNxzLBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:12.168257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03218","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb32565569db43afdf56d8a4abe07072e6eb8efb744b85edd23376b76f0aa85","sha256:0c853ffbe0d97be93c2452a01a6f4019939f18f1ba471cec7156ae2a73f1ca52"],"state_sha256":"a286739d0fc8299a425563935865f209f702f87ab926e12608eaf2cf32f03b4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upq7PPBqXWM52sMaTiScaS8/C8Vnq4vpvHHYp0jZSnI2Hol3csB9FvjF77w3Su+jXgjT0sv6krwfM0bLD1ozAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:19:29.710285Z","bundle_sha256":"d9cf9ccecc6cc83af23b8be23a0d07a5dc16a7bd6460eb4db32663c5dc25c7c0"}}