{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XHD3RI3SCQWMT3TVQUX5MFQSRN","short_pith_number":"pith:XHD3RI3S","canonical_record":{"source":{"id":"1202.2549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:19:13Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"9bf69fe525d838584360bc3874d6ef555de2e672ae117fef4ed437e71b1d0e26","abstract_canon_sha256":"14d6d2e9bfb4ca2e1c23b940300392ac5783b015314eb35a13795ee3fb1b89a3"},"schema_version":"1.0"},"canonical_sha256":"b9c7b8a372142cc9ee75852fd616128b77944fb12c17864aba2c134ba2585997","source":{"kind":"arxiv","id":"1202.2549","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2549","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2549v2","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2549","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"XHD3RI3SCQWM","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XHD3RI3SCQWMT3TV","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XHD3RI3S","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XHD3RI3SCQWMT3TVQUX5MFQSRN","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:19:13Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"9bf69fe525d838584360bc3874d6ef555de2e672ae117fef4ed437e71b1d0e26","abstract_canon_sha256":"14d6d2e9bfb4ca2e1c23b940300392ac5783b015314eb35a13795ee3fb1b89a3"},"schema_version":"1.0"},"canonical_sha256":"b9c7b8a372142cc9ee75852fd616128b77944fb12c17864aba2c134ba2585997","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:30.897633Z","signature_b64":"OD2Au3PcsIpuClnyfs9GGKijbwf0vds0meh10Jcw6ACoq9rNG5dH4wElhaaVUeGGGdf4pf18Zi0jplTNl03BCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c7b8a372142cc9ee75852fd616128b77944fb12c17864aba2c134ba2585997","last_reissued_at":"2026-05-18T01:58:30.897188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:30.897188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2549","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":"2026-05-18T01:58:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rOLiPCGIm0YBRphUkkp0mICM9K41eNnmTBM4qOaB5RMFgIC3sfpJn+4z56GZY1QJIzrKHxYpmcAVXnMbUu4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:45:14.971857Z"},"content_sha256":"e7c3e10f6bcc1fd919b531a18cee330fc12030a2e8db3348517ed7162786cca1","schema_version":"1.0","event_id":"sha256:e7c3e10f6bcc1fd919b531a18cee330fc12030a2e8db3348517ed7162786cca1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XHD3RI3SCQWMT3TVQUX5MFQSRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact scaling in the expansion-modification system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.PR","authors_text":"Edgardo Ugalde, Ra\\'ul Salgado-Garc\\'ia","submitted_at":"2012-02-12T17:19:13Z","abstract_excerpt":"This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a \\emph{mutation probability}. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a signi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2549","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":"2026-05-18T01:58:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"soA9tUnAZtHWW15nXgrTzdgCjmlKsl2+76gsCYDlaQKAZcilv7k0NuC2swCZBC2jx2TQgHP9rRUf7zaKIfizDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:45:14.972514Z"},"content_sha256":"f9a0f06aaaa0de9fbb5e5fd9336cd16c05185788f65c4881a2bb2b8ee860be44","schema_version":"1.0","event_id":"sha256:f9a0f06aaaa0de9fbb5e5fd9336cd16c05185788f65c4881a2bb2b8ee860be44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/bundle.json","state_url":"https://pith.science/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/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":"2026-06-06T23:45:14Z","links":{"resolver":"https://pith.science/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN","bundle":"https://pith.science/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/bundle.json","state":"https://pith.science/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHD3RI3SCQWMT3TVQUX5MFQSRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XHD3RI3SCQWMT3TVQUX5MFQSRN","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":"14d6d2e9bfb4ca2e1c23b940300392ac5783b015314eb35a13795ee3fb1b89a3","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:19:13Z","title_canon_sha256":"9bf69fe525d838584360bc3874d6ef555de2e672ae117fef4ed437e71b1d0e26"},"schema_version":"1.0","source":{"id":"1202.2549","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2549","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2549v2","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2549","created_at":"2026-05-18T01:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"XHD3RI3SCQWM","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XHD3RI3SCQWMT3TV","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XHD3RI3S","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:f9a0f06aaaa0de9fbb5e5fd9336cd16c05185788f65c4881a2bb2b8ee860be44","target":"graph","created_at":"2026-05-18T01:58:30Z","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":"This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a \\emph{mutation probability}. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a signi","authors_text":"Edgardo Ugalde, Ra\\'ul Salgado-Garc\\'ia","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:19:13Z","title":"Exact scaling in the expansion-modification system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2549","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:e7c3e10f6bcc1fd919b531a18cee330fc12030a2e8db3348517ed7162786cca1","target":"record","created_at":"2026-05-18T01:58:30Z","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":"14d6d2e9bfb4ca2e1c23b940300392ac5783b015314eb35a13795ee3fb1b89a3","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-12T17:19:13Z","title_canon_sha256":"9bf69fe525d838584360bc3874d6ef555de2e672ae117fef4ed437e71b1d0e26"},"schema_version":"1.0","source":{"id":"1202.2549","kind":"arxiv","version":2}},"canonical_sha256":"b9c7b8a372142cc9ee75852fd616128b77944fb12c17864aba2c134ba2585997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9c7b8a372142cc9ee75852fd616128b77944fb12c17864aba2c134ba2585997","first_computed_at":"2026-05-18T01:58:30.897188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:30.897188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OD2Au3PcsIpuClnyfs9GGKijbwf0vds0meh10Jcw6ACoq9rNG5dH4wElhaaVUeGGGdf4pf18Zi0jplTNl03BCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:30.897633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2549","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7c3e10f6bcc1fd919b531a18cee330fc12030a2e8db3348517ed7162786cca1","sha256:f9a0f06aaaa0de9fbb5e5fd9336cd16c05185788f65c4881a2bb2b8ee860be44"],"state_sha256":"70b1fdd1c83cf4c2be4701ffa027271d81eb54069d9e17705e7292684f49ed9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vv/Qy3nN1z6BFBKLUAGI3werODJc9Wry1zbtXNCmrfAOHqlkDIzKaHUKebDfskRwdPEaK7yEWIBKyV9Ljf+gBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:45:14.976218Z","bundle_sha256":"794838a0904a8c9772068c30b94b8e851852df6788df3abd12cfd0bc6d35e9ab"}}