{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6EP5TONVYJPYG6HUBSIZQHGHMB","short_pith_number":"pith:6EP5TONV","canonical_record":{"source":{"id":"1701.04564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-17T08:31:59Z","cross_cats_sorted":[],"title_canon_sha256":"ba5ee42ac42f32a6bcb8858bde1d3d6abce644cddb30c811fc72d2eadd9585b9","abstract_canon_sha256":"2d9962ac3cf2fbb755ae0accca75ab42bcd7ded70d5fb0588e1a564c6832182b"},"schema_version":"1.0"},"canonical_sha256":"f11fd9b9b5c25f8378f40c91981cc76048d5fbd0aed47eec36904ecd738ca5dc","source":{"kind":"arxiv","id":"1701.04564","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04564","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04564v2","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04564","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"6EP5TONVYJPY","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6EP5TONVYJPYG6HU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6EP5TONV","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6EP5TONVYJPYG6HUBSIZQHGHMB","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-17T08:31:59Z","cross_cats_sorted":[],"title_canon_sha256":"ba5ee42ac42f32a6bcb8858bde1d3d6abce644cddb30c811fc72d2eadd9585b9","abstract_canon_sha256":"2d9962ac3cf2fbb755ae0accca75ab42bcd7ded70d5fb0588e1a564c6832182b"},"schema_version":"1.0"},"canonical_sha256":"f11fd9b9b5c25f8378f40c91981cc76048d5fbd0aed47eec36904ecd738ca5dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:54.991891Z","signature_b64":"ep8mGbEdrxSWXTuLA6PSXLfn1vketAvIWUXpJ6b0igSZ6kTdG43MvYPjkEkv2cBU6jTIidW6GijEfu7o71+LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f11fd9b9b5c25f8378f40c91981cc76048d5fbd0aed47eec36904ecd738ca5dc","last_reissued_at":"2026-05-18T00:17:54.991162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:54.991162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04564","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":"2026-05-18T00:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdfQ+et8Nd3tNLhhzi80093jNc1ybwTHjvvw0EvXIEHgq9/lDpYXvRTu0BKcplcjxnZ0oAN22+8hEQbfLq6IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:02:02.926556Z"},"content_sha256":"c2fed804f74876daad80b5d14d4cd878fdbb590295da767b1adcf8b0ecdf4d68","schema_version":"1.0","event_id":"sha256:c2fed804f74876daad80b5d14d4cd878fdbb590295da767b1adcf8b0ecdf4d68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6EP5TONVYJPYG6HUBSIZQHGHMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical study of branching and stability of solutions to three-dimensional martensitic phase transformations using gradient-regularized, non-convex, finite strain elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Koki Sagiyama, Krishna Garikipati, Shiva Rudraraju","submitted_at":"2017-01-17T08:31:59Z","abstract_excerpt":"In the setting of continuum elasticity, phase transformations involving martensitic variants are modeled by a free energy density function that is non-convex in strain space. Here, we adopt an existing mathematical model in which we regularize the non-convex free energy density function by higher-order gradient terms at finite strain and derive boundary value problems via the standard variational argument applied to the corresponding total free energy, inspired by Toupin's theory of gradient elasticity. These gradient terms are to preclude existence of arbitrarily fine microstructures, while s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04564","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":"2026-05-18T00:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0Udv7LVs5W+BOkBeU58HLxh84f9CH7BKPye9aWFuM6EjWy4k3efN/9j9FbxjUn3q7RXfwerflj+WWECBHIEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:02:02.926902Z"},"content_sha256":"6ea7b5e3a951163c677a9f06e9618fabbae300c5acb0ff24ec523e5a257daf9f","schema_version":"1.0","event_id":"sha256:6ea7b5e3a951163c677a9f06e9618fabbae300c5acb0ff24ec523e5a257daf9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/bundle.json","state_url":"https://pith.science/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/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":"2026-06-03T05:02:02Z","links":{"resolver":"https://pith.science/pith/6EP5TONVYJPYG6HUBSIZQHGHMB","bundle":"https://pith.science/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/bundle.json","state":"https://pith.science/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EP5TONVYJPYG6HUBSIZQHGHMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6EP5TONVYJPYG6HUBSIZQHGHMB","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":"2d9962ac3cf2fbb755ae0accca75ab42bcd7ded70d5fb0588e1a564c6832182b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-17T08:31:59Z","title_canon_sha256":"ba5ee42ac42f32a6bcb8858bde1d3d6abce644cddb30c811fc72d2eadd9585b9"},"schema_version":"1.0","source":{"id":"1701.04564","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04564","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04564v2","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04564","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"6EP5TONVYJPY","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6EP5TONVYJPYG6HU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6EP5TONV","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6ea7b5e3a951163c677a9f06e9618fabbae300c5acb0ff24ec523e5a257daf9f","target":"graph","created_at":"2026-05-18T00:17:54Z","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":"In the setting of continuum elasticity, phase transformations involving martensitic variants are modeled by a free energy density function that is non-convex in strain space. Here, we adopt an existing mathematical model in which we regularize the non-convex free energy density function by higher-order gradient terms at finite strain and derive boundary value problems via the standard variational argument applied to the corresponding total free energy, inspired by Toupin's theory of gradient elasticity. These gradient terms are to preclude existence of arbitrarily fine microstructures, while s","authors_text":"Koki Sagiyama, Krishna Garikipati, Shiva Rudraraju","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-17T08:31:59Z","title":"A numerical study of branching and stability of solutions to three-dimensional martensitic phase transformations using gradient-regularized, non-convex, finite strain elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04564","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:c2fed804f74876daad80b5d14d4cd878fdbb590295da767b1adcf8b0ecdf4d68","target":"record","created_at":"2026-05-18T00:17:54Z","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":"2d9962ac3cf2fbb755ae0accca75ab42bcd7ded70d5fb0588e1a564c6832182b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-17T08:31:59Z","title_canon_sha256":"ba5ee42ac42f32a6bcb8858bde1d3d6abce644cddb30c811fc72d2eadd9585b9"},"schema_version":"1.0","source":{"id":"1701.04564","kind":"arxiv","version":2}},"canonical_sha256":"f11fd9b9b5c25f8378f40c91981cc76048d5fbd0aed47eec36904ecd738ca5dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f11fd9b9b5c25f8378f40c91981cc76048d5fbd0aed47eec36904ecd738ca5dc","first_computed_at":"2026-05-18T00:17:54.991162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:54.991162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ep8mGbEdrxSWXTuLA6PSXLfn1vketAvIWUXpJ6b0igSZ6kTdG43MvYPjkEkv2cBU6jTIidW6GijEfu7o71+LAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:54.991891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04564","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2fed804f74876daad80b5d14d4cd878fdbb590295da767b1adcf8b0ecdf4d68","sha256:6ea7b5e3a951163c677a9f06e9618fabbae300c5acb0ff24ec523e5a257daf9f"],"state_sha256":"54317e97606448bd3e166e1ae1f31e8f397f8e934c18eb768e802007d81ef188"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9pFEgdlhpejhj/iAckYD/P2EAfxGuy3YdcxAIZcZir6rxrmMLWf6ahghCvn+meL9U0l1QtnS0MWG8QVkxvPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:02:02.928909Z","bundle_sha256":"0083f8f8e31e4f9d0f31de9d26000faa9f6f33f2d7243a755e3cd7c345afe667"}}