{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QE4NHWNKYZ7EWR4MFZ4TX55CMI","short_pith_number":"pith:QE4NHWNK","canonical_record":{"source":{"id":"1903.11654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-27T19:06:45Z","cross_cats_sorted":[],"title_canon_sha256":"c87726dd11b335e1a272e8b643375454249817cc54e97bd7072b55cd614105ee","abstract_canon_sha256":"c6be1d9058d2b6fdd2b12820063fd8c56ef9b9552fee0ea31a6588d6fcb102df"},"schema_version":"1.0"},"canonical_sha256":"8138d3d9aac67e4b478c2e793bf7a2623b3879caf2af80714c845df78c3f5ba1","source":{"kind":"arxiv","id":"1903.11654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11654","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11654v2","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11654","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"QE4NHWNKYZ7E","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QE4NHWNKYZ7EWR4M","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QE4NHWNK","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QE4NHWNKYZ7EWR4MFZ4TX55CMI","target":"record","payload":{"canonical_record":{"source":{"id":"1903.11654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-27T19:06:45Z","cross_cats_sorted":[],"title_canon_sha256":"c87726dd11b335e1a272e8b643375454249817cc54e97bd7072b55cd614105ee","abstract_canon_sha256":"c6be1d9058d2b6fdd2b12820063fd8c56ef9b9552fee0ea31a6588d6fcb102df"},"schema_version":"1.0"},"canonical_sha256":"8138d3d9aac67e4b478c2e793bf7a2623b3879caf2af80714c845df78c3f5ba1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:49.632664Z","signature_b64":"06u2HwWhvSPc2rmFbxxVIJMeqhV4G9UurxO7AB5WCaL/NIymoHFUQllQGAX/pQQDJHOAk0uSGK9QSOMykf+jAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8138d3d9aac67e4b478c2e793bf7a2623b3879caf2af80714c845df78c3f5ba1","last_reissued_at":"2026-05-17T23:49:49.632144Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:49.632144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.11654","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b920b9OUB5Cnt72nseC8BgkdJSNcAc/9A/GwmoPezl1ziZP+kOSNyHb7j3Xo+qEirbX5lRjHJiLgcZ45sBecAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:07:58.234026Z"},"content_sha256":"211185f337d716f6e90c245cdacb9cc3f4fc5117cb20458d77bc672cf6e310f4","schema_version":"1.0","event_id":"sha256:211185f337d716f6e90c245cdacb9cc3f4fc5117cb20458d77bc672cf6e310f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QE4NHWNKYZ7EWR4MFZ4TX55CMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit time-discretisation of elastodynamics with some inelastic processes at small strains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christos Panagiotopoulos, Chrysoula Tsogka, Tomas Roubicek","submitted_at":"2019-03-27T19:06:45Z","abstract_excerpt":"The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems involving some internal variables subjected to a dissipative evolution. After spatial discretisation, a-priori estimates and convergence is proved under the usual CFL-condition. Applications to specific problems in continuum mechanics of solids at small stains are considered, in particular linearized plasticity, diffusion in poroelastic media, damage, or adhes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11654","kind":"arxiv","version":2},"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":"2026-05-17T23:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qk/L1qPDujTrhfJybQks1BP4McDz39FLGUgpf7pDM2Wodxmg8AEdRk+/RSDnW+1qvhN514ld7Al13/7nkO8EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:07:58.234399Z"},"content_sha256":"a3d49aab757b71e0c3a2d74d17ce491d592bd18e2a58a8429f37d5026eeff32d","schema_version":"1.0","event_id":"sha256:a3d49aab757b71e0c3a2d74d17ce491d592bd18e2a58a8429f37d5026eeff32d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/bundle.json","state_url":"https://pith.science/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/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":"2026-06-03T12:07:58Z","links":{"resolver":"https://pith.science/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI","bundle":"https://pith.science/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/bundle.json","state":"https://pith.science/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QE4NHWNKYZ7EWR4MFZ4TX55CMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QE4NHWNKYZ7EWR4MFZ4TX55CMI","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":"c6be1d9058d2b6fdd2b12820063fd8c56ef9b9552fee0ea31a6588d6fcb102df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-27T19:06:45Z","title_canon_sha256":"c87726dd11b335e1a272e8b643375454249817cc54e97bd7072b55cd614105ee"},"schema_version":"1.0","source":{"id":"1903.11654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11654","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11654v2","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11654","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"QE4NHWNKYZ7E","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QE4NHWNKYZ7EWR4M","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QE4NHWNK","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:a3d49aab757b71e0c3a2d74d17ce491d592bd18e2a58a8429f37d5026eeff32d","target":"graph","created_at":"2026-05-17T23:49:49Z","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":"The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems involving some internal variables subjected to a dissipative evolution. After spatial discretisation, a-priori estimates and convergence is proved under the usual CFL-condition. Applications to specific problems in continuum mechanics of solids at small stains are considered, in particular linearized plasticity, diffusion in poroelastic media, damage, or adhes","authors_text":"Christos Panagiotopoulos, Chrysoula Tsogka, Tomas Roubicek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-27T19:06:45Z","title":"Explicit time-discretisation of elastodynamics with some inelastic processes at small strains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11654","kind":"arxiv","version":2},"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":"sha256:211185f337d716f6e90c245cdacb9cc3f4fc5117cb20458d77bc672cf6e310f4","target":"record","created_at":"2026-05-17T23:49:49Z","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":"c6be1d9058d2b6fdd2b12820063fd8c56ef9b9552fee0ea31a6588d6fcb102df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-27T19:06:45Z","title_canon_sha256":"c87726dd11b335e1a272e8b643375454249817cc54e97bd7072b55cd614105ee"},"schema_version":"1.0","source":{"id":"1903.11654","kind":"arxiv","version":2}},"canonical_sha256":"8138d3d9aac67e4b478c2e793bf7a2623b3879caf2af80714c845df78c3f5ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8138d3d9aac67e4b478c2e793bf7a2623b3879caf2af80714c845df78c3f5ba1","first_computed_at":"2026-05-17T23:49:49.632144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:49.632144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"06u2HwWhvSPc2rmFbxxVIJMeqhV4G9UurxO7AB5WCaL/NIymoHFUQllQGAX/pQQDJHOAk0uSGK9QSOMykf+jAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:49.632664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:211185f337d716f6e90c245cdacb9cc3f4fc5117cb20458d77bc672cf6e310f4","sha256:a3d49aab757b71e0c3a2d74d17ce491d592bd18e2a58a8429f37d5026eeff32d"],"state_sha256":"8f4dd130b5ea90c87aceaeb3c447eb3e401bd590ece88db664f907c501d0c604"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7qqHTA7RvWAdvDjp3TuuKSaOvaQ1w2EeGIjqv2JbpeXLoi8IUpBy5ScMM7Ku21CaVZPZcf1S6sIH4RC19NBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:07:58.236588Z","bundle_sha256":"fe58bbdb77a005aa524c27096fc6aeee7c8c21f205ddb1d9c41d704cc30a98f0"}}