{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CI4L3OWAULWGUVJOLLXARQ3IQM","short_pith_number":"pith:CI4L3OWA","canonical_record":{"source":{"id":"1510.04303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-14T20:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"5b2c36a93d83ef1c0d3470760f83700663e5fe409e1db541e7bedc834388c9e2","abstract_canon_sha256":"be1a23e80c0722c2c4793363538c6017f2c782a654cdeaa30bd6ee0b1b7ca7bb"},"schema_version":"1.0"},"canonical_sha256":"1238bdbac0a2ec6a552e5aee08c368832d4b54ac0d3f6558e88c54108e8465e4","source":{"kind":"arxiv","id":"1510.04303","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04303","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04303v1","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04303","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"CI4L3OWAULWG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CI4L3OWAULWGUVJO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CI4L3OWA","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CI4L3OWAULWGUVJOLLXARQ3IQM","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-14T20:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"5b2c36a93d83ef1c0d3470760f83700663e5fe409e1db541e7bedc834388c9e2","abstract_canon_sha256":"be1a23e80c0722c2c4793363538c6017f2c782a654cdeaa30bd6ee0b1b7ca7bb"},"schema_version":"1.0"},"canonical_sha256":"1238bdbac0a2ec6a552e5aee08c368832d4b54ac0d3f6558e88c54108e8465e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:07.544052Z","signature_b64":"FNDYu1bBx86IZw3dpiLYVh/q1714OYjxR5icyK+7ZyXzDirMcOQGokdkCMWCwnexuqHLgmpkjuBC/NugwokhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1238bdbac0a2ec6a552e5aee08c368832d4b54ac0d3f6558e88c54108e8465e4","last_reissued_at":"2026-05-18T01:30:07.543481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:07.543481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04303","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":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3RxEepRzUGroXes/BTHKiIIZMqsA/NYRv2spoby7nNBzJ1BX2hf2WOOwqztOx8edE7YSru13Uu51WMd4ZblDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:45:15.339681Z"},"content_sha256":"9f3dde15a07cce7d7019801b178eec0d14557e6b650c85c7cfe3155ef1871a85","schema_version":"1.0","event_id":"sha256:9f3dde15a07cce7d7019801b178eec0d14557e6b650c85c7cfe3155ef1871a85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CI4L3OWAULWGUVJOLLXARQ3IQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alessandro Della Rocca, Luca Bonaventura","submitted_at":"2015-10-14T20:35:40Z","abstract_excerpt":"We analyze the one-step method TR-BDF2 from the point of view of monotonicity, strong stability and positivity. All these properties are strongly related and reviewed in the common framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. Two hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy and maximize the absolute monotonicity radius, while keeping the native L-stability useful in stiff problems. Nume"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04303","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":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcHL+8rVt75GijyqDDNMizoKzorXRW6XUnO02xbdarvYwgMCnWH7TaokbnaFaNZo85DGMefTlukAVTKYMmHvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:45:15.340017Z"},"content_sha256":"2e01ccc570f4ff2f1c736241d06cab5db25bbf84a874ef9a67660bc5232965f3","schema_version":"1.0","event_id":"sha256:2e01ccc570f4ff2f1c736241d06cab5db25bbf84a874ef9a67660bc5232965f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/bundle.json","state_url":"https://pith.science/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/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":"2026-06-25T09:45:15Z","links":{"resolver":"https://pith.science/pith/CI4L3OWAULWGUVJOLLXARQ3IQM","bundle":"https://pith.science/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/bundle.json","state":"https://pith.science/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CI4L3OWAULWGUVJOLLXARQ3IQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CI4L3OWAULWGUVJOLLXARQ3IQM","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":"be1a23e80c0722c2c4793363538c6017f2c782a654cdeaa30bd6ee0b1b7ca7bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-14T20:35:40Z","title_canon_sha256":"5b2c36a93d83ef1c0d3470760f83700663e5fe409e1db541e7bedc834388c9e2"},"schema_version":"1.0","source":{"id":"1510.04303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04303","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04303v1","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04303","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"CI4L3OWAULWG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CI4L3OWAULWGUVJO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CI4L3OWA","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:2e01ccc570f4ff2f1c736241d06cab5db25bbf84a874ef9a67660bc5232965f3","target":"graph","created_at":"2026-05-18T01:30:07Z","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 analyze the one-step method TR-BDF2 from the point of view of monotonicity, strong stability and positivity. All these properties are strongly related and reviewed in the common framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. Two hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy and maximize the absolute monotonicity radius, while keeping the native L-stability useful in stiff problems. Nume","authors_text":"Alessandro Della Rocca, Luca Bonaventura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-14T20:35:40Z","title":"Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04303","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":"sha256:9f3dde15a07cce7d7019801b178eec0d14557e6b650c85c7cfe3155ef1871a85","target":"record","created_at":"2026-05-18T01:30:07Z","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":"be1a23e80c0722c2c4793363538c6017f2c782a654cdeaa30bd6ee0b1b7ca7bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-14T20:35:40Z","title_canon_sha256":"5b2c36a93d83ef1c0d3470760f83700663e5fe409e1db541e7bedc834388c9e2"},"schema_version":"1.0","source":{"id":"1510.04303","kind":"arxiv","version":1}},"canonical_sha256":"1238bdbac0a2ec6a552e5aee08c368832d4b54ac0d3f6558e88c54108e8465e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1238bdbac0a2ec6a552e5aee08c368832d4b54ac0d3f6558e88c54108e8465e4","first_computed_at":"2026-05-18T01:30:07.543481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:07.543481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FNDYu1bBx86IZw3dpiLYVh/q1714OYjxR5icyK+7ZyXzDirMcOQGokdkCMWCwnexuqHLgmpkjuBC/NugwokhCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:07.544052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f3dde15a07cce7d7019801b178eec0d14557e6b650c85c7cfe3155ef1871a85","sha256:2e01ccc570f4ff2f1c736241d06cab5db25bbf84a874ef9a67660bc5232965f3"],"state_sha256":"6cc99646d4e6febc4a4f6d801e0d906fd25c0c54d52933b39b56f1d3f058560b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UhXYbc1mjVLc9P+4v0UF+kfrHkx74ea89nz4cqu0MQMM61LG5gZ7KZsbUMY3LuwDNuw1oqq7PS5Aj6GKIUXBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:45:15.343359Z","bundle_sha256":"c28ce3e0e08d644ce3934c65fafff70ba52aa6d513f031e9b868247224006961"}}