{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZMKXANGZOWIDBQTYEWOMDTZEJK","short_pith_number":"pith:ZMKXANGZ","canonical_record":{"source":{"id":"1503.00927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T12:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"948c16581adc82e9133b36ee868d80ceb92f1e826edb39c5bebaf5a8912fbe19","abstract_canon_sha256":"21e107057aaa6bd4b599aa80bd2794459e57f49455c890a690436d13dbd80a8b"},"schema_version":"1.0"},"canonical_sha256":"cb157034d9759030c278259cc1cf244a8fcadfc2b0b0bfbcb6c73d8362000b90","source":{"kind":"arxiv","id":"1503.00927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00927","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00927v1","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00927","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZMKXANGZOWID","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMKXANGZOWIDBQTY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMKXANGZ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZMKXANGZOWIDBQTYEWOMDTZEJK","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T12:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"948c16581adc82e9133b36ee868d80ceb92f1e826edb39c5bebaf5a8912fbe19","abstract_canon_sha256":"21e107057aaa6bd4b599aa80bd2794459e57f49455c890a690436d13dbd80a8b"},"schema_version":"1.0"},"canonical_sha256":"cb157034d9759030c278259cc1cf244a8fcadfc2b0b0bfbcb6c73d8362000b90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:48.083657Z","signature_b64":"5D7yx3nNV8VkSTvALv9vtL370TBah/VtSynibSYn39kxsMr6RUv+o4MngKqEsnB2RdCleqjYzn1d/VltGoY8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb157034d9759030c278259cc1cf244a8fcadfc2b0b0bfbcb6c73d8362000b90","last_reissued_at":"2026-05-18T02:25:48.083186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:48.083186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00927","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":"2026-05-18T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/l9/MwuTU4VshIDiD1sOHcTxDKQNzRYmghuyBx0sP5IsXU1BiqsEaeCIKOLrceeCiUPRyX/fptVon0vb5vCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:39:45.621021Z"},"content_sha256":"722398385c60c5b7c6111ebee813f425164fe1406136ce7086d07b31e86e1b4d","schema_version":"1.0","event_id":"sha256:722398385c60c5b7c6111ebee813f425164fe1406136ce7086d07b31e86e1b4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZMKXANGZOWIDBQTYEWOMDTZEJK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisabetta Rocca, Gianni Gilardi, J\\\"urgen Sprekels, Pierluigi Colli","submitted_at":"2015-03-03T12:56:15Z","abstract_excerpt":"This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in the recent contributions arXiv:1401.5943 [math.AP] and arXiv:1501.07057 [math.AP] from the viewpoint of well-posedness, long time behavior and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, we continue the analysis performed in arXiv:1501.07057 [math.AP] by showing two indepen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00927","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":"2026-05-18T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zEQkj6h2lnUp8tUbfnoHEkukKIO0YVwPQLtP+JJcPNbWdfaEGjBREocEvohMH8AGM4OZJ9jTvFJ21+t5vIIlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:39:45.621475Z"},"content_sha256":"80e29fe3a18afab4ebc7a656cc8f4d458b411d31a57f7665a83f02463825c835","schema_version":"1.0","event_id":"sha256:80e29fe3a18afab4ebc7a656cc8f4d458b411d31a57f7665a83f02463825c835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/bundle.json","state_url":"https://pith.science/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/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":"2026-05-27T00:39:45Z","links":{"resolver":"https://pith.science/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK","bundle":"https://pith.science/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/bundle.json","state":"https://pith.science/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMKXANGZOWIDBQTYEWOMDTZEJK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZMKXANGZOWIDBQTYEWOMDTZEJK","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":"21e107057aaa6bd4b599aa80bd2794459e57f49455c890a690436d13dbd80a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T12:56:15Z","title_canon_sha256":"948c16581adc82e9133b36ee868d80ceb92f1e826edb39c5bebaf5a8912fbe19"},"schema_version":"1.0","source":{"id":"1503.00927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00927","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00927v1","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00927","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZMKXANGZOWID","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMKXANGZOWIDBQTY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMKXANGZ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:80e29fe3a18afab4ebc7a656cc8f4d458b411d31a57f7665a83f02463825c835","target":"graph","created_at":"2026-05-18T02:25:48Z","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 paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in the recent contributions arXiv:1401.5943 [math.AP] and arXiv:1501.07057 [math.AP] from the viewpoint of well-posedness, long time behavior and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, we continue the analysis performed in arXiv:1501.07057 [math.AP] by showing two indepen","authors_text":"Elisabetta Rocca, Gianni Gilardi, J\\\"urgen Sprekels, Pierluigi Colli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T12:56:15Z","title":"Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00927","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":"sha256:722398385c60c5b7c6111ebee813f425164fe1406136ce7086d07b31e86e1b4d","target":"record","created_at":"2026-05-18T02:25:48Z","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":"21e107057aaa6bd4b599aa80bd2794459e57f49455c890a690436d13dbd80a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T12:56:15Z","title_canon_sha256":"948c16581adc82e9133b36ee868d80ceb92f1e826edb39c5bebaf5a8912fbe19"},"schema_version":"1.0","source":{"id":"1503.00927","kind":"arxiv","version":1}},"canonical_sha256":"cb157034d9759030c278259cc1cf244a8fcadfc2b0b0bfbcb6c73d8362000b90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb157034d9759030c278259cc1cf244a8fcadfc2b0b0bfbcb6c73d8362000b90","first_computed_at":"2026-05-18T02:25:48.083186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:48.083186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5D7yx3nNV8VkSTvALv9vtL370TBah/VtSynibSYn39kxsMr6RUv+o4MngKqEsnB2RdCleqjYzn1d/VltGoY8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:48.083657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722398385c60c5b7c6111ebee813f425164fe1406136ce7086d07b31e86e1b4d","sha256:80e29fe3a18afab4ebc7a656cc8f4d458b411d31a57f7665a83f02463825c835"],"state_sha256":"bb48befc8708c6c355838a8b05fdabbb0fc70e5ac90736e9d7aded016f8b4d39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xc5IybdpaPUbwq3I12TU9LYW4bJqW1mZcbi5eSAIWtxmZO0KL0pokJMlzgqESxef4ZH82e7yoyy6flN6PrDzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:39:45.623788Z","bundle_sha256":"6e5229e22ebd0d8a3642ec834060edea7e322896dab10aa2c32f856998efdbd9"}}