{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:72TC7USOBQN6GV3WHWIGR4ASC6","short_pith_number":"pith:72TC7USO","canonical_record":{"source":{"id":"1204.1329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-05T19:49:42Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"acca095855c15419a26091d1039e9e9d5e5767c19feedfd600c3c13d06d60dae","abstract_canon_sha256":"97efd41870b5bfa241a3e276c22235215c07af09a465cdfc4bd249d825ad362e"},"schema_version":"1.0"},"canonical_sha256":"fea62fd24e0c1be357763d9068f01217ae309a394f7697dae55f6a1470498c86","source":{"kind":"arxiv","id":"1204.1329","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1329","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1329v2","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1329","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"72TC7USOBQN6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"72TC7USOBQN6GV3W","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"72TC7USO","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:72TC7USOBQN6GV3WHWIGR4ASC6","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-05T19:49:42Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"acca095855c15419a26091d1039e9e9d5e5767c19feedfd600c3c13d06d60dae","abstract_canon_sha256":"97efd41870b5bfa241a3e276c22235215c07af09a465cdfc4bd249d825ad362e"},"schema_version":"1.0"},"canonical_sha256":"fea62fd24e0c1be357763d9068f01217ae309a394f7697dae55f6a1470498c86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:25.977964Z","signature_b64":"yGn3rsYMFq9mU21bfrz49P0RL98McTRJGYnlV5l6gPiEhcwqa2JkMMABffAYawbq0Ykuk9TL2YPjZitaEbrKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fea62fd24e0c1be357763d9068f01217ae309a394f7697dae55f6a1470498c86","last_reissued_at":"2026-05-18T03:35:25.977177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:25.977177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1329","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":"2026-05-18T03:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHtlKodmCAgHX0/AcKjSmX1uQCX0P9A/i6GsTcPBnfrxckPDSc0toyHnNNQawAeRkmzjxt8Kdse7C64UCbEmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:52:00.245134Z"},"content_sha256":"f8e525d3430cade17ac92d3d0c1d655a4ee0d6a54747862837478bdecee7bf19","schema_version":"1.0","event_id":"sha256:f8e525d3430cade17ac92d3d0c1d655a4ee0d6a54747862837478bdecee7bf19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:72TC7USOBQN6GV3WHWIGR4ASC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hon Wai Lau, Maya Paczuski, Peter Grassberger","submitted_at":"2012-04-05T19:49:42Z","abstract_excerpt":"Ordinary bond percolation (OP) can be viewed as a process where clusters grow by joining them pairwise, by adding links chosen randomly one by one from a set of predefined `virtual' links. In contrast, in agglomerative percolation (AP) clusters grow by choosing randomly a `target cluster' and joining it with all its neighbors, as defined by the same set of virtual links. Previous studies showed that AP is in different universality classes from OP for several types of (virtual) networks (linear chains, trees, Erdos-Renyi networks), but most surprising were the results for 2-d lattices: While AP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1329","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":"2026-05-18T03:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GeHaFQn8U//JMLsw0eVS6su9ngb44ut8wBETiNdh0eUH8YwoTeQuCJO4Js8RCjUE3YG7MhCbiskDw2pWPFwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:52:00.245821Z"},"content_sha256":"aeb72af31cc4fa0b1ba0398367371ec9ff6c2f1a9dd0abb9c5ed1bd4fd75beed","schema_version":"1.0","event_id":"sha256:aeb72af31cc4fa0b1ba0398367371ec9ff6c2f1a9dd0abb9c5ed1bd4fd75beed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72TC7USOBQN6GV3WHWIGR4ASC6/bundle.json","state_url":"https://pith.science/pith/72TC7USOBQN6GV3WHWIGR4ASC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72TC7USOBQN6GV3WHWIGR4ASC6/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":"2026-05-25T19:52:00Z","links":{"resolver":"https://pith.science/pith/72TC7USOBQN6GV3WHWIGR4ASC6","bundle":"https://pith.science/pith/72TC7USOBQN6GV3WHWIGR4ASC6/bundle.json","state":"https://pith.science/pith/72TC7USOBQN6GV3WHWIGR4ASC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72TC7USOBQN6GV3WHWIGR4ASC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:72TC7USOBQN6GV3WHWIGR4ASC6","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":"97efd41870b5bfa241a3e276c22235215c07af09a465cdfc4bd249d825ad362e","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-05T19:49:42Z","title_canon_sha256":"acca095855c15419a26091d1039e9e9d5e5767c19feedfd600c3c13d06d60dae"},"schema_version":"1.0","source":{"id":"1204.1329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1329","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1329v2","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1329","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"72TC7USOBQN6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"72TC7USOBQN6GV3W","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"72TC7USO","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:aeb72af31cc4fa0b1ba0398367371ec9ff6c2f1a9dd0abb9c5ed1bd4fd75beed","target":"graph","created_at":"2026-05-18T03:35:25Z","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":"Ordinary bond percolation (OP) can be viewed as a process where clusters grow by joining them pairwise, by adding links chosen randomly one by one from a set of predefined `virtual' links. In contrast, in agglomerative percolation (AP) clusters grow by choosing randomly a `target cluster' and joining it with all its neighbors, as defined by the same set of virtual links. Previous studies showed that AP is in different universality classes from OP for several types of (virtual) networks (linear chains, trees, Erdos-Renyi networks), but most surprising were the results for 2-d lattices: While AP","authors_text":"Hon Wai Lau, Maya Paczuski, Peter Grassberger","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-05T19:49:42Z","title":"Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1329","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:f8e525d3430cade17ac92d3d0c1d655a4ee0d6a54747862837478bdecee7bf19","target":"record","created_at":"2026-05-18T03:35:25Z","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":"97efd41870b5bfa241a3e276c22235215c07af09a465cdfc4bd249d825ad362e","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-05T19:49:42Z","title_canon_sha256":"acca095855c15419a26091d1039e9e9d5e5767c19feedfd600c3c13d06d60dae"},"schema_version":"1.0","source":{"id":"1204.1329","kind":"arxiv","version":2}},"canonical_sha256":"fea62fd24e0c1be357763d9068f01217ae309a394f7697dae55f6a1470498c86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fea62fd24e0c1be357763d9068f01217ae309a394f7697dae55f6a1470498c86","first_computed_at":"2026-05-18T03:35:25.977177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:25.977177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGn3rsYMFq9mU21bfrz49P0RL98McTRJGYnlV5l6gPiEhcwqa2JkMMABffAYawbq0Ykuk9TL2YPjZitaEbrKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:25.977964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8e525d3430cade17ac92d3d0c1d655a4ee0d6a54747862837478bdecee7bf19","sha256:aeb72af31cc4fa0b1ba0398367371ec9ff6c2f1a9dd0abb9c5ed1bd4fd75beed"],"state_sha256":"9f675f760203c7ecfbcba9987ca097b2f0efe99200dd2b00642b2f12e71941b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTXvckln9nuh3vOy7DKM4CW8E2y/R2g/fTA0wXZCziTmgLQpt06R3onH1jLzVGU9cUGbbJmRZkm5SdxFe9VmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:52:00.249437Z","bundle_sha256":"d809fbb8b4fa91ac85bbb7141918f89b8217b66558d15ba5d5f0f79d0f7631ff"}}