{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:TQ7XNP6SWAHDTMNY47XBX7J3DM","short_pith_number":"pith:TQ7XNP6S","canonical_record":{"source":{"id":"0912.3904","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-19T16:13:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1bf01f8b1d8eb332b0714a990644d7265a2cc88b728478a17045509e99d72ea0","abstract_canon_sha256":"b23c6f391d9069b71ad95e42214e2240c6c5052706083236e943303ac4d70bea"},"schema_version":"1.0"},"canonical_sha256":"9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c","source":{"kind":"arxiv","id":"0912.3904","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3904","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3904v5","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3904","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"TQ7XNP6SWAHD","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TQ7XNP6SWAHDTMNY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TQ7XNP6S","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:TQ7XNP6SWAHDTMNY47XBX7J3DM","target":"record","payload":{"canonical_record":{"source":{"id":"0912.3904","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-19T16:13:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1bf01f8b1d8eb332b0714a990644d7265a2cc88b728478a17045509e99d72ea0","abstract_canon_sha256":"b23c6f391d9069b71ad95e42214e2240c6c5052706083236e943303ac4d70bea"},"schema_version":"1.0"},"canonical_sha256":"9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:01.038792Z","signature_b64":"LarAatrUgQMOk7VYGYv4H0AXZ/rNku9OQTIvoYyGGGTDgIhRWTXunHWRc57mZcbvc/khn57cv2Mv1bYUHNdoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c","last_reissued_at":"2026-05-18T03:57:01.038084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:01.038084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.3904","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4wR64F0h674Wv39If66CUcWokgB8JHFmsMkiqJ4fCRvrpXGbB0A0B2tZlAihREqtqFFjAuAA1V2CD/jeRyBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:44:53.538721Z"},"content_sha256":"9659208abdcd23c2bb83a054a87fc0182023764bcc02c82fd432321ed0148532","schema_version":"1.0","event_id":"sha256:9659208abdcd23c2bb83a054a87fc0182023764bcc02c82fd432321ed0148532"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:TQ7XNP6SWAHDTMNY47XBX7J3DM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Balazs Rath","submitted_at":"2009-12-19T16:13:32Z","abstract_excerpt":"We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting models where the sequence of initial multigraphs is convergent in a sense which is a natural generalization of the notion of convergence of dense graph sequences, defined by Lovasz and Szegedy in arXiv:math/0408173. We investigate how the limit object evolves under the edge reconnecting dynamics if we rescale time properly: we give the complete c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3904","kind":"arxiv","version":5},"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":"2026-05-18T03:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQPWUE+entcVeMKsgsk+CVyu9Ve0Kz4BfA2VE445DfcbdGJ91CFu06lDj8SjANBm3M+SRVkmPdXD1xjdM2KaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:44:53.539265Z"},"content_sha256":"a5c7f7e9e5507b893d1ff72385c68648a14d4c40d10ea4365553acb81d14fcb1","schema_version":"1.0","event_id":"sha256:a5c7f7e9e5507b893d1ff72385c68648a14d4c40d10ea4365553acb81d14fcb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/bundle.json","state_url":"https://pith.science/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/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":"2026-06-04T22:44:53Z","links":{"resolver":"https://pith.science/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM","bundle":"https://pith.science/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/bundle.json","state":"https://pith.science/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQ7XNP6SWAHDTMNY47XBX7J3DM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TQ7XNP6SWAHDTMNY47XBX7J3DM","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":"b23c6f391d9069b71ad95e42214e2240c6c5052706083236e943303ac4d70bea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-19T16:13:32Z","title_canon_sha256":"1bf01f8b1d8eb332b0714a990644d7265a2cc88b728478a17045509e99d72ea0"},"schema_version":"1.0","source":{"id":"0912.3904","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3904","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3904v5","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3904","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"TQ7XNP6SWAHD","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TQ7XNP6SWAHDTMNY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TQ7XNP6S","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:a5c7f7e9e5507b893d1ff72385c68648a14d4c40d10ea4365553acb81d14fcb1","target":"graph","created_at":"2026-05-18T03:57:01Z","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 define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting models where the sequence of initial multigraphs is convergent in a sense which is a natural generalization of the notion of convergence of dense graph sequences, defined by Lovasz and Szegedy in arXiv:math/0408173. We investigate how the limit object evolves under the edge reconnecting dynamics if we rescale time properly: we give the complete c","authors_text":"Balazs Rath","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-19T16:13:32Z","title":"Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3904","kind":"arxiv","version":5},"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":"sha256:9659208abdcd23c2bb83a054a87fc0182023764bcc02c82fd432321ed0148532","target":"record","created_at":"2026-05-18T03:57:01Z","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":"b23c6f391d9069b71ad95e42214e2240c6c5052706083236e943303ac4d70bea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-19T16:13:32Z","title_canon_sha256":"1bf01f8b1d8eb332b0714a990644d7265a2cc88b728478a17045509e99d72ea0"},"schema_version":"1.0","source":{"id":"0912.3904","kind":"arxiv","version":5}},"canonical_sha256":"9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c","first_computed_at":"2026-05-18T03:57:01.038084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:01.038084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LarAatrUgQMOk7VYGYv4H0AXZ/rNku9OQTIvoYyGGGTDgIhRWTXunHWRc57mZcbvc/khn57cv2Mv1bYUHNdoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:01.038792Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3904","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9659208abdcd23c2bb83a054a87fc0182023764bcc02c82fd432321ed0148532","sha256:a5c7f7e9e5507b893d1ff72385c68648a14d4c40d10ea4365553acb81d14fcb1"],"state_sha256":"741366f6e098b64ecf982d02494a8f570360bdd238effbe332bd8c5a66ca4898"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1V4b4Z4t7m1S5HvouYyYzRREM/t2PQUFwptf1E0a7aTpqBynI9r5eaGmPzi274XT4P2Y/+S+1C6x9DHpJFsKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:44:53.542018Z","bundle_sha256":"d6f2cf7d9c36e6c99eda9e0fd4c371e6fa8af27979784b7f9b78c8b9fac7ddbb"}}