{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:2ODE6EPZYVOEQBLDYKPKZA2ZK5","short_pith_number":"pith:2ODE6EPZ","canonical_record":{"source":{"id":"nlin/0002039","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2000-02-22T21:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"44609b8eb75aed4e65e897b55644fcc3a3b515784f2affd889cfddb914262fdf","abstract_canon_sha256":"4fd24b9671c523c12f3e3b3ea40a48888b3b7369897c1d0d91278296580dc547"},"schema_version":"1.0"},"canonical_sha256":"d3864f11f9c55c480563c29eac8359575157e5611b2dc1c5236b2b36b3794e4d","source":{"kind":"arxiv","id":"nlin/0002039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0002039","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0002039v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0002039","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"2ODE6EPZYVOE","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"2ODE6EPZYVOEQBLD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"2ODE6EPZ","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:2ODE6EPZYVOEQBLDYKPKZA2ZK5","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0002039","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2000-02-22T21:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"44609b8eb75aed4e65e897b55644fcc3a3b515784f2affd889cfddb914262fdf","abstract_canon_sha256":"4fd24b9671c523c12f3e3b3ea40a48888b3b7369897c1d0d91278296580dc547"},"schema_version":"1.0"},"canonical_sha256":"d3864f11f9c55c480563c29eac8359575157e5611b2dc1c5236b2b36b3794e4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.279620Z","signature_b64":"Z5QwG3kNvYuxD1XJ2W6bq8BD4ovJXbPrOuEoqHxYQgyS7B6zFn3cULOJlC1Qb/KZnnJXndQWmE38HbeOzPLsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3864f11f9c55c480563c29eac8359575157e5611b2dc1c5236b2b36b3794e4d","last_reissued_at":"2026-05-18T01:05:22.279174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.279174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0002039","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":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7LKF38jTdpOXfs46s6F9pVAeMBRz4gfVBVzvXYxXz+eo7sdOBrvPGSabgpSUO4wW64S94kpe7Rtvipme8eKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:24:09.330730Z"},"content_sha256":"4022a403be9d021ed5360627448a27e3766c3113bc2aeb87b0c8c822408311e7","schema_version":"1.0","event_id":"sha256:4022a403be9d021ed5360627448a27e3766c3113bc2aeb87b0c8c822408311e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:2ODE6EPZYVOEQBLDYKPKZA2ZK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Front motion for phase transitions in systems with memory","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Alexander I. Domoshnitsky, Alexander Nepomnyashchy, Horacio G. Rotstein","submitted_at":"2000-02-22T21:10:31Z","abstract_excerpt":"We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic one, the damped Klein-Gordon equation. By means of a formal asymptotic analysis we show that to the leading order and under suitable assumptions on the kernels, the integro-differential equation behave like a hyperbolic partial differential equation obtained by considering prototype kernels: the evolution of fronts is governed by the extended, damped Born-Infe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0002039","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":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n3sUKtPvZV2NzUOCvrj06TM9gKrqzpZfWDgxBiVImW5rmh2jhNNxMpMXApV5m7dQHOoK6ml4A+Zl7e/bUf7sDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:24:09.331140Z"},"content_sha256":"9a8a1e040bcc0f173554002e8f623ea24acb02b360b178c28b8e8e7d78ee95e1","schema_version":"1.0","event_id":"sha256:9a8a1e040bcc0f173554002e8f623ea24acb02b360b178c28b8e8e7d78ee95e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/bundle.json","state_url":"https://pith.science/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/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":"2026-06-01T21:24:09Z","links":{"resolver":"https://pith.science/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5","bundle":"https://pith.science/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/bundle.json","state":"https://pith.science/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ODE6EPZYVOEQBLDYKPKZA2ZK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:2ODE6EPZYVOEQBLDYKPKZA2ZK5","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":"4fd24b9671c523c12f3e3b3ea40a48888b3b7369897c1d0d91278296580dc547","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2000-02-22T21:10:31Z","title_canon_sha256":"44609b8eb75aed4e65e897b55644fcc3a3b515784f2affd889cfddb914262fdf"},"schema_version":"1.0","source":{"id":"nlin/0002039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0002039","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0002039v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0002039","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"2ODE6EPZYVOE","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"2ODE6EPZYVOEQBLD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"2ODE6EPZ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:9a8a1e040bcc0f173554002e8f623ea24acb02b360b178c28b8e8e7d78ee95e1","target":"graph","created_at":"2026-05-18T01:05:22Z","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 the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic one, the damped Klein-Gordon equation. By means of a formal asymptotic analysis we show that to the leading order and under suitable assumptions on the kernels, the integro-differential equation behave like a hyperbolic partial differential equation obtained by considering prototype kernels: the evolution of fronts is governed by the extended, damped Born-Infe","authors_text":"Alexander I. Domoshnitsky, Alexander Nepomnyashchy, Horacio G. Rotstein","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2000-02-22T21:10:31Z","title":"Front motion for phase transitions in systems with memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0002039","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":"sha256:4022a403be9d021ed5360627448a27e3766c3113bc2aeb87b0c8c822408311e7","target":"record","created_at":"2026-05-18T01:05:22Z","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":"4fd24b9671c523c12f3e3b3ea40a48888b3b7369897c1d0d91278296580dc547","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2000-02-22T21:10:31Z","title_canon_sha256":"44609b8eb75aed4e65e897b55644fcc3a3b515784f2affd889cfddb914262fdf"},"schema_version":"1.0","source":{"id":"nlin/0002039","kind":"arxiv","version":1}},"canonical_sha256":"d3864f11f9c55c480563c29eac8359575157e5611b2dc1c5236b2b36b3794e4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3864f11f9c55c480563c29eac8359575157e5611b2dc1c5236b2b36b3794e4d","first_computed_at":"2026-05-18T01:05:22.279174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.279174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5QwG3kNvYuxD1XJ2W6bq8BD4ovJXbPrOuEoqHxYQgyS7B6zFn3cULOJlC1Qb/KZnnJXndQWmE38HbeOzPLsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.279620Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0002039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4022a403be9d021ed5360627448a27e3766c3113bc2aeb87b0c8c822408311e7","sha256:9a8a1e040bcc0f173554002e8f623ea24acb02b360b178c28b8e8e7d78ee95e1"],"state_sha256":"711727f55014a1340aef2904366095d21a4c8d06a74b075c10b44f25b093b513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bp7pM/5wLXeEAzhY5w4aynDGZNMWWpNPx4Sryx5F/eJlN03egsSWn/Ub8EgKRnrcLsZt44+sTaaVumBpWv8yBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:24:09.333293Z","bundle_sha256":"98bc6c8d90dad1b2e111c067812cd686748558dc440e067059542720da560e30"}}