{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NTWBBSYSDOTEYL4P7FOB3JR7WR","short_pith_number":"pith:NTWBBSYS","canonical_record":{"source":{"id":"1203.0472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-03-02T14:17:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9c7501bc81e82c42f61fcb542f6e89e891679a070abd4b09d7045657784113b0","abstract_canon_sha256":"91147acedf306e7387202ea4ccfd5c858811dd10a0253b9b43f2fe07153c1704"},"schema_version":"1.0"},"canonical_sha256":"6cec10cb121ba64c2f8ff95c1da63fb47c3c91e9a7afe443c3ff1f1a29a4e8b1","source":{"kind":"arxiv","id":"1203.0472","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0472","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0472v1","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0472","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"NTWBBSYSDOTE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NTWBBSYSDOTEYL4P","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NTWBBSYS","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NTWBBSYSDOTEYL4P7FOB3JR7WR","target":"record","payload":{"canonical_record":{"source":{"id":"1203.0472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-03-02T14:17:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9c7501bc81e82c42f61fcb542f6e89e891679a070abd4b09d7045657784113b0","abstract_canon_sha256":"91147acedf306e7387202ea4ccfd5c858811dd10a0253b9b43f2fe07153c1704"},"schema_version":"1.0"},"canonical_sha256":"6cec10cb121ba64c2f8ff95c1da63fb47c3c91e9a7afe443c3ff1f1a29a4e8b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:00.621166Z","signature_b64":"K2COuTT2MzdzAAKXAMbHB3/mgAufL1hz0MGt/OwNKZFUVrW6wXfu5NbsO/Mcz61PgRIiswONwwT5Ie46AGevBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cec10cb121ba64c2f8ff95c1da63fb47c3c91e9a7afe443c3ff1f1a29a4e8b1","last_reissued_at":"2026-05-18T04:01:00.620419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:00.620419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.0472","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":"2026-05-18T04:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtABsg73n8qg4shTntpnmJ7pIPQNz7Z+vCYPh9xzWU2CJU3P84qusPCgDdf292viU2ucBQzsOsf5rG/H8+jpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:28:25.371003Z"},"content_sha256":"c1cc60c241850cda54993c8eaae8796baa2fc8af78b29455c80e70216197bfb6","schema_version":"1.0","event_id":"sha256:c1cc60c241850cda54993c8eaae8796baa2fc8af78b29455c80e70216197bfb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NTWBBSYSDOTEYL4P7FOB3JR7WR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hereditary models of polymers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"M.De Angelis","submitted_at":"2012-03-02T14:17:59Z","abstract_excerpt":"An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator L1 whose behavior is now available. Moreover, properties typical of wave hierarchies can be applied to polymeric materials. As an example the case n= 2 is considered and results are applied to the Rouse model and the reptation model which describe different aspects of polymer chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0472","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":"2026-05-18T04:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OdyupI1cysDgEQNDccbduBoPFRT2AmA4JZ5FiCE1WcN3tEpinKpPOdXF7dlikgN83ffLPHChkM5cEekc1R8/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:28:25.371421Z"},"content_sha256":"878a52c26dd7b0ad061dae51b3cd2509cc63209a5a33fd454a1bc194d30145eb","schema_version":"1.0","event_id":"sha256:878a52c26dd7b0ad061dae51b3cd2509cc63209a5a33fd454a1bc194d30145eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/bundle.json","state_url":"https://pith.science/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/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":"2026-06-10T22:28:25Z","links":{"resolver":"https://pith.science/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR","bundle":"https://pith.science/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/bundle.json","state":"https://pith.science/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTWBBSYSDOTEYL4P7FOB3JR7WR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NTWBBSYSDOTEYL4P7FOB3JR7WR","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":"91147acedf306e7387202ea4ccfd5c858811dd10a0253b9b43f2fe07153c1704","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-03-02T14:17:59Z","title_canon_sha256":"9c7501bc81e82c42f61fcb542f6e89e891679a070abd4b09d7045657784113b0"},"schema_version":"1.0","source":{"id":"1203.0472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0472","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0472v1","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0472","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"NTWBBSYSDOTE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NTWBBSYSDOTEYL4P","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NTWBBSYS","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:878a52c26dd7b0ad061dae51b3cd2509cc63209a5a33fd454a1bc194d30145eb","target":"graph","created_at":"2026-05-18T04:01:00Z","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":"An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator L1 whose behavior is now available. Moreover, properties typical of wave hierarchies can be applied to polymeric materials. As an example the case n= 2 is considered and results are applied to the Rouse model and the reptation model which describe different aspects of polymer chains.","authors_text":"M.De Angelis","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-03-02T14:17:59Z","title":"On hereditary models of polymers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0472","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:c1cc60c241850cda54993c8eaae8796baa2fc8af78b29455c80e70216197bfb6","target":"record","created_at":"2026-05-18T04:01:00Z","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":"91147acedf306e7387202ea4ccfd5c858811dd10a0253b9b43f2fe07153c1704","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-03-02T14:17:59Z","title_canon_sha256":"9c7501bc81e82c42f61fcb542f6e89e891679a070abd4b09d7045657784113b0"},"schema_version":"1.0","source":{"id":"1203.0472","kind":"arxiv","version":1}},"canonical_sha256":"6cec10cb121ba64c2f8ff95c1da63fb47c3c91e9a7afe443c3ff1f1a29a4e8b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cec10cb121ba64c2f8ff95c1da63fb47c3c91e9a7afe443c3ff1f1a29a4e8b1","first_computed_at":"2026-05-18T04:01:00.620419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:00.620419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2COuTT2MzdzAAKXAMbHB3/mgAufL1hz0MGt/OwNKZFUVrW6wXfu5NbsO/Mcz61PgRIiswONwwT5Ie46AGevBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:00.621166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1cc60c241850cda54993c8eaae8796baa2fc8af78b29455c80e70216197bfb6","sha256:878a52c26dd7b0ad061dae51b3cd2509cc63209a5a33fd454a1bc194d30145eb"],"state_sha256":"d6e2f8e865d82a0bb0f0b7bc7bad36f58d1ad0009ec9ae71b53cdf0118ada307"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9e+tcmGG2vE0Us5D7ORaHKD6Q5JpamgHOY6ewFb1lV3tOxj83UXsnAJSGfbR0T/Nt3rRBR4n3Ud/30aDeX2bAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:28:25.373797Z","bundle_sha256":"eaaea3baeaadd6ac18198fce481e25823128356b3d3ac8d498052556ffc67e3b"}}