{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4UIHONGHMFVZ5ZUAAPYJHR4HG6","short_pith_number":"pith:4UIHONGH","canonical_record":{"source":{"id":"0812.4843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-28T19:55:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"43dcf55db05a6aa0d31de9dfd0fa3dde806a26ccd186152ba108c765309b5730","abstract_canon_sha256":"83bf9348c34c4fcac131518af2318b00ddde5971b2aac81feea86429f2b536aa"},"schema_version":"1.0"},"canonical_sha256":"e5107734c7616b9ee68003f093c78737a830297ae8673dd6b39c96aac49852e6","source":{"kind":"arxiv","id":"0812.4843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4843","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4843v1","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4843","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"4UIHONGHMFVZ","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"4UIHONGHMFVZ5ZUA","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"4UIHONGH","created_at":"2026-06-03T23:06:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4UIHONGHMFVZ5ZUAAPYJHR4HG6","target":"record","payload":{"canonical_record":{"source":{"id":"0812.4843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-28T19:55:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"43dcf55db05a6aa0d31de9dfd0fa3dde806a26ccd186152ba108c765309b5730","abstract_canon_sha256":"83bf9348c34c4fcac131518af2318b00ddde5971b2aac81feea86429f2b536aa"},"schema_version":"1.0"},"canonical_sha256":"e5107734c7616b9ee68003f093c78737a830297ae8673dd6b39c96aac49852e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:10.133957Z","signature_b64":"+CO1uZyDjWfrfUafTEX7yetnycT6A4Jdam9cy3P4fCrbJqAlx9FDbq1nd3BbPnxRIfcTkarJlkr28GBBLIItAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5107734c7616b9ee68003f093c78737a830297ae8673dd6b39c96aac49852e6","last_reissued_at":"2026-06-03T23:06:10.133545Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:10.133545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.4843","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":"2026-06-03T23:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tc3yuYuERb/Q+b1vwxkd+e6M3xlXmiqCNMgCL4EyHAbUKb9SGOrbT92xpjOCyTCQRe5Y/7lnaN9KBtc3rI7JAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:58:44.299769Z"},"content_sha256":"6fd5d26345e4955534f20a18f02833e802fd461a65d6953a6d9c6ec700474a1e","schema_version":"1.0","event_id":"sha256:6fd5d26345e4955534f20a18f02833e802fd461a65d6953a6d9c6ec700474a1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4UIHONGHMFVZ5ZUAAPYJHR4HG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Matthew Dobson, Mitchell Luskin","submitted_at":"2008-12-28T19:55:21Z","abstract_excerpt":"We give an analysis of a continuation algorithm for the numerical solution of the force-based quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner.\n  The analysis presented in this paper is used to determine an efficient strategy for the parameter step size and number of iterations at each parameter value to achieve a solution to a required tolerance. We present computational results for the deformation of a Lennard-Jones chain under tension to d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4843","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/0812.4843/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":"2026-06-03T23:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rP+GOQtcHxyP2Tynbvm30vSQ8ffY4Ex8bnDyz+AbHY47MaaIF/oADevEOcFiIP72BXUE/Pxj1iPyAPUQtMDiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:58:44.300142Z"},"content_sha256":"3d2aeb9fb1b872d6480e852720bd3af623364d2ebafa7e1996bc668f5814f6b7","schema_version":"1.0","event_id":"sha256:3d2aeb9fb1b872d6480e852720bd3af623364d2ebafa7e1996bc668f5814f6b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/bundle.json","state_url":"https://pith.science/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/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":"2026-06-20T22:58:44Z","links":{"resolver":"https://pith.science/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6","bundle":"https://pith.science/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/bundle.json","state":"https://pith.science/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4UIHONGHMFVZ5ZUAAPYJHR4HG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4UIHONGHMFVZ5ZUAAPYJHR4HG6","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":"83bf9348c34c4fcac131518af2318b00ddde5971b2aac81feea86429f2b536aa","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-28T19:55:21Z","title_canon_sha256":"43dcf55db05a6aa0d31de9dfd0fa3dde806a26ccd186152ba108c765309b5730"},"schema_version":"1.0","source":{"id":"0812.4843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4843","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4843v1","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4843","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"4UIHONGHMFVZ","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"4UIHONGHMFVZ5ZUA","created_at":"2026-06-03T23:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"4UIHONGH","created_at":"2026-06-03T23:06:10Z"}],"graph_snapshots":[{"event_id":"sha256:3d2aeb9fb1b872d6480e852720bd3af623364d2ebafa7e1996bc668f5814f6b7","target":"graph","created_at":"2026-06-03T23:06:10Z","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/0812.4843/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an analysis of a continuation algorithm for the numerical solution of the force-based quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner.\n  The analysis presented in this paper is used to determine an efficient strategy for the parameter step size and number of iterations at each parameter value to achieve a solution to a required tolerance. We present computational results for the deformation of a Lennard-Jones chain under tension to d","authors_text":"Matthew Dobson, Mitchell Luskin","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-28T19:55:21Z","title":"Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4843","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":"sha256:6fd5d26345e4955534f20a18f02833e802fd461a65d6953a6d9c6ec700474a1e","target":"record","created_at":"2026-06-03T23:06:10Z","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":"83bf9348c34c4fcac131518af2318b00ddde5971b2aac81feea86429f2b536aa","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-28T19:55:21Z","title_canon_sha256":"43dcf55db05a6aa0d31de9dfd0fa3dde806a26ccd186152ba108c765309b5730"},"schema_version":"1.0","source":{"id":"0812.4843","kind":"arxiv","version":1}},"canonical_sha256":"e5107734c7616b9ee68003f093c78737a830297ae8673dd6b39c96aac49852e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5107734c7616b9ee68003f093c78737a830297ae8673dd6b39c96aac49852e6","first_computed_at":"2026-06-03T23:06:10.133545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:10.133545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CO1uZyDjWfrfUafTEX7yetnycT6A4Jdam9cy3P4fCrbJqAlx9FDbq1nd3BbPnxRIfcTkarJlkr28GBBLIItAw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:10.133957Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fd5d26345e4955534f20a18f02833e802fd461a65d6953a6d9c6ec700474a1e","sha256:3d2aeb9fb1b872d6480e852720bd3af623364d2ebafa7e1996bc668f5814f6b7"],"state_sha256":"28569f0ae3616e29a1d51ee2dc75ad2b8476697bbf35d8176683f03555253bd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9psxa4FXeukqguFe+gWX2wEhhUvCwcwBs/hihQ7OfeMGHQBsd+wSlVDX3/NstlZHBEUSLx7CAO1R8on0/HbJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:58:44.302149Z","bundle_sha256":"bead15da7b6e31a17097fe12acd01a456250270ae772690346155b2ebadd75ce"}}