{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3IMNVN7M4ELJFE3QGNND3F5ZNF","short_pith_number":"pith:3IMNVN7M","canonical_record":{"source":{"id":"2501.16968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-28T14:12:05Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4ecfc12384466910d32d4754e5cf0b3ab04f8ea9e695e9bb0cab06454187393e","abstract_canon_sha256":"0cc355f79242b98089280503f47761e12eef0149a1f6ed8efa6a2f09125ad441"},"schema_version":"1.0"},"canonical_sha256":"da18dab7ece116929370335a3d97b9694fc4bb1534051180ee7c43263b2dcdcc","source":{"kind":"arxiv","id":"2501.16968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16968","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16968v1","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16968","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"3IMNVN7M4ELJ","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"3IMNVN7M4ELJFE3Q","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"3IMNVN7M","created_at":"2026-07-05T10:06:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3IMNVN7M4ELJFE3QGNND3F5ZNF","target":"record","payload":{"canonical_record":{"source":{"id":"2501.16968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-28T14:12:05Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4ecfc12384466910d32d4754e5cf0b3ab04f8ea9e695e9bb0cab06454187393e","abstract_canon_sha256":"0cc355f79242b98089280503f47761e12eef0149a1f6ed8efa6a2f09125ad441"},"schema_version":"1.0"},"canonical_sha256":"da18dab7ece116929370335a3d97b9694fc4bb1534051180ee7c43263b2dcdcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:06:20.966293Z","signature_b64":"455lCTjsGtDOpo/xbid9zzABEijVQhfiMm02DEfZegf179d5QEofLX7W5uUjKPbewS0jZo1Z7VsLqRFmncunCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da18dab7ece116929370335a3d97b9694fc4bb1534051180ee7c43263b2dcdcc","last_reissued_at":"2026-07-05T10:06:20.965853Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:06:20.965853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.16968","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":"2026-07-05T10:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMyKXFjLugJt3nkvHpFUfPFjtcTud2gcIdunE58d9noTdYeOcfPqkA72F/wVDbUeRh4mzRGOsIJ7LhVUJq64Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T14:12:19.785073Z"},"content_sha256":"48f6bd8a62c7886a87654696d8c05b9daa28f70d75221f588fe12952ea03b654","schema_version":"1.0","event_id":"sha256:48f6bd8a62c7886a87654696d8c05b9daa28f70d75221f588fe12952ea03b654"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3IMNVN7M4ELJFE3QGNND3F5ZNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"AT1 fourth-order isogeometric phase-field modeling of brittle fracture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alessandro Reali, Alessia Patton, Eleonora Maggiorelli, Luigi Greco, Matteo Negri","submitted_at":"2025-01-28T14:12:05Z","abstract_excerpt":"A crucial aspect in phase-field modeling, based on the variational formulation of brittle fracture, is the accurate representation of how the fracture surface energy is dissipated during the fracture process in the energy competition within a minimization problem. In general, the family of AT1 functionals showcases a well-defined elastic limit and narrow transition regions before crack onset, as opposed to AT2 models. On the other hand, high-order functionals provide similar accuracy as low-order ones but allow for larger mesh sizes in their discretization, remarkably reducing the computationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16968","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.16968/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbVqGRKL1o81LE6AOSLY7JExnT9o0V5x/EMqYS/2kLhzi7pGf2djpHE4lZPty8Jl9ZCyGV2nIvROAb3Q4C6bDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T14:12:19.785601Z"},"content_sha256":"f2d85c2e2d616ce3b025f244cd39d4b95a0ca4d59d0480a1fce12f030aaad67d","schema_version":"1.0","event_id":"sha256:f2d85c2e2d616ce3b025f244cd39d4b95a0ca4d59d0480a1fce12f030aaad67d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/bundle.json","state_url":"https://pith.science/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/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":"2026-08-07T14:12:19Z","links":{"resolver":"https://pith.science/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF","bundle":"https://pith.science/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/bundle.json","state":"https://pith.science/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IMNVN7M4ELJFE3QGNND3F5ZNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3IMNVN7M4ELJFE3QGNND3F5ZNF","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":"0cc355f79242b98089280503f47761e12eef0149a1f6ed8efa6a2f09125ad441","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-28T14:12:05Z","title_canon_sha256":"4ecfc12384466910d32d4754e5cf0b3ab04f8ea9e695e9bb0cab06454187393e"},"schema_version":"1.0","source":{"id":"2501.16968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16968","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16968v1","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16968","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"3IMNVN7M4ELJ","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"3IMNVN7M4ELJFE3Q","created_at":"2026-07-05T10:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"3IMNVN7M","created_at":"2026-07-05T10:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:f2d85c2e2d616ce3b025f244cd39d4b95a0ca4d59d0480a1fce12f030aaad67d","target":"graph","created_at":"2026-07-05T10:06:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.16968/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A crucial aspect in phase-field modeling, based on the variational formulation of brittle fracture, is the accurate representation of how the fracture surface energy is dissipated during the fracture process in the energy competition within a minimization problem. In general, the family of AT1 functionals showcases a well-defined elastic limit and narrow transition regions before crack onset, as opposed to AT2 models. On the other hand, high-order functionals provide similar accuracy as low-order ones but allow for larger mesh sizes in their discretization, remarkably reducing the computationa","authors_text":"Alessandro Reali, Alessia Patton, Eleonora Maggiorelli, Luigi Greco, Matteo Negri","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-28T14:12:05Z","title":"AT1 fourth-order isogeometric phase-field modeling of brittle fracture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16968","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":"sha256:48f6bd8a62c7886a87654696d8c05b9daa28f70d75221f588fe12952ea03b654","target":"record","created_at":"2026-07-05T10:06:20Z","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":"0cc355f79242b98089280503f47761e12eef0149a1f6ed8efa6a2f09125ad441","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-28T14:12:05Z","title_canon_sha256":"4ecfc12384466910d32d4754e5cf0b3ab04f8ea9e695e9bb0cab06454187393e"},"schema_version":"1.0","source":{"id":"2501.16968","kind":"arxiv","version":1}},"canonical_sha256":"da18dab7ece116929370335a3d97b9694fc4bb1534051180ee7c43263b2dcdcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da18dab7ece116929370335a3d97b9694fc4bb1534051180ee7c43263b2dcdcc","first_computed_at":"2026-07-05T10:06:20.965853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:20.965853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"455lCTjsGtDOpo/xbid9zzABEijVQhfiMm02DEfZegf179d5QEofLX7W5uUjKPbewS0jZo1Z7VsLqRFmncunCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:20.966293Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.16968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48f6bd8a62c7886a87654696d8c05b9daa28f70d75221f588fe12952ea03b654","sha256:f2d85c2e2d616ce3b025f244cd39d4b95a0ca4d59d0480a1fce12f030aaad67d"],"state_sha256":"4974907b17816e1f0cc72ced8a67ab675c53f10b7a2a19a00927018e6c85d227"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lm3uNgK9zMIAoD4X859xEimUqbcHmAkvhusZz5U47uYM8oqHMxBqIh+oXrgon5oPjZMqJmALCxDZk5uaUoetBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T14:12:19.796825Z","bundle_sha256":"c6cae6de661a59ef47537de69b22a67961ae30a2f6b097663d35bb0210bfb865"}}