{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C4DOPHMGF42O66D4XRUSPASL33","short_pith_number":"pith:C4DOPHMG","canonical_record":{"source":{"id":"1507.07388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"90d1a307594d8f686d6b3517dcb11e2f145d06eaf3a716b0900250147e96fbb8","abstract_canon_sha256":"9c83b6333a40d087b144789ce8bbc77d0d76c2fd4e6e7810ef564f7042b7e018"},"schema_version":"1.0"},"canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","source":{"kind":"arxiv","id":"1507.07388","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07388","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07388v2","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07388","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"C4DOPHMGF42O","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C4DOPHMGF42O66D4","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C4DOPHMG","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C4DOPHMGF42O66D4XRUSPASL33","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"90d1a307594d8f686d6b3517dcb11e2f145d06eaf3a716b0900250147e96fbb8","abstract_canon_sha256":"9c83b6333a40d087b144789ce8bbc77d0d76c2fd4e6e7810ef564f7042b7e018"},"schema_version":"1.0"},"canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:45.725474Z","signature_b64":"YI5zSjb5HpPMCTQM+QFfdCipu9b223TNK+tyZinLjiiaC6HX5qBQW1zrnpwxjuKeFdO9BUETPwhOs5QCG/9dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","last_reissued_at":"2026-05-18T01:20:45.724759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:45.724759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07388","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":"2026-05-18T01:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRqkdaTxRKXjjA1kIL6lhVUqyckfL5RLDsIezHVnC4drV8pv26MOUm0ycsdyrsLltIW/M5ugjyWE9WjNd6zfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:18:29.513056Z"},"content_sha256":"4e8aeb1646f5bbf7235c7629153c2b7731d9da0191f4af260d3c4c5e901d9f72","schema_version":"1.0","event_id":"sha256:4e8aeb1646f5bbf7235c7629153c2b7731d9da0191f4af260d3c4c5e901d9f72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C4DOPHMGF42O66D4XRUSPASL33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An ellipticity domain for the distortional Hencky-logarithmic strain energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin","submitted_at":"2015-07-27T12:52:34Z","abstract_excerpt":"We describe ellipticity domains for the isochoric elastic energy $ F\\mapsto \\|{\\rm dev}_n\\log U\\|^2=\\bigg\\|\\log \\frac{\\sqrt{F^TF}}{(\\det F)^{1/n}}\\bigg\\|^2 =\\frac{1}{4}\\,\\bigg\\|\\log \\frac{C}{({\\rm det} C)^{1/n}}\\bigg\\|^2 $ for $n=2,3$, where $C=F^TF$ for $F\\in {\\rm GL}^+(n)$. Here, ${\\rm dev}_n\\log {U} =\\log {U}-\\frac{1}{n}\\, {\\rm tr}(\\log {U})\\cdot 1\\!\\!1$ is the deviatoric part of the logarithmic strain tensor $\\log U$. For $n=2$ we identify the maximal ellipticity domain, while for $n=3$ we show that the energy is Legendre-Hadamard elliptic in the set $\\mathcal{E}_3\\bigg(W_{_{\\rm H}}^{\\rm i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07388","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":"2026-05-18T01:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t606TDLj3GLqYBJg54vkEptyFkFvvOECh2G6b5u9mB5tllrnvPQFdy0iB+3X8N0IUWBhoYSMmJOGkLI1PTa8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:18:29.513416Z"},"content_sha256":"090d55fd912872b87118847241796655ce4af6b45adb2a8217790a96f835dd57","schema_version":"1.0","event_id":"sha256:090d55fd912872b87118847241796655ce4af6b45adb2a8217790a96f835dd57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4DOPHMGF42O66D4XRUSPASL33/bundle.json","state_url":"https://pith.science/pith/C4DOPHMGF42O66D4XRUSPASL33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4DOPHMGF42O66D4XRUSPASL33/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":"2026-05-28T02:18:29Z","links":{"resolver":"https://pith.science/pith/C4DOPHMGF42O66D4XRUSPASL33","bundle":"https://pith.science/pith/C4DOPHMGF42O66D4XRUSPASL33/bundle.json","state":"https://pith.science/pith/C4DOPHMGF42O66D4XRUSPASL33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4DOPHMGF42O66D4XRUSPASL33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C4DOPHMGF42O66D4XRUSPASL33","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":"9c83b6333a40d087b144789ce8bbc77d0d76c2fd4e6e7810ef564f7042b7e018","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","title_canon_sha256":"90d1a307594d8f686d6b3517dcb11e2f145d06eaf3a716b0900250147e96fbb8"},"schema_version":"1.0","source":{"id":"1507.07388","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07388","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07388v2","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07388","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"C4DOPHMGF42O","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C4DOPHMGF42O66D4","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C4DOPHMG","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:090d55fd912872b87118847241796655ce4af6b45adb2a8217790a96f835dd57","target":"graph","created_at":"2026-05-18T01:20:45Z","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 describe ellipticity domains for the isochoric elastic energy $ F\\mapsto \\|{\\rm dev}_n\\log U\\|^2=\\bigg\\|\\log \\frac{\\sqrt{F^TF}}{(\\det F)^{1/n}}\\bigg\\|^2 =\\frac{1}{4}\\,\\bigg\\|\\log \\frac{C}{({\\rm det} C)^{1/n}}\\bigg\\|^2 $ for $n=2,3$, where $C=F^TF$ for $F\\in {\\rm GL}^+(n)$. Here, ${\\rm dev}_n\\log {U} =\\log {U}-\\frac{1}{n}\\, {\\rm tr}(\\log {U})\\cdot 1\\!\\!1$ is the deviatoric part of the logarithmic strain tensor $\\log U$. For $n=2$ we identify the maximal ellipticity domain, while for $n=3$ we show that the energy is Legendre-Hadamard elliptic in the set $\\mathcal{E}_3\\bigg(W_{_{\\rm H}}^{\\rm i","authors_text":"Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","title":"An ellipticity domain for the distortional Hencky-logarithmic strain energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07388","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":"sha256:4e8aeb1646f5bbf7235c7629153c2b7731d9da0191f4af260d3c4c5e901d9f72","target":"record","created_at":"2026-05-18T01:20:45Z","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":"9c83b6333a40d087b144789ce8bbc77d0d76c2fd4e6e7810ef564f7042b7e018","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-27T12:52:34Z","title_canon_sha256":"90d1a307594d8f686d6b3517dcb11e2f145d06eaf3a716b0900250147e96fbb8"},"schema_version":"1.0","source":{"id":"1507.07388","kind":"arxiv","version":2}},"canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1706e79d862f34ef787cbc6927824bdef1be620dfa21de74b240a2c9832fa5ad","first_computed_at":"2026-05-18T01:20:45.724759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:45.724759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YI5zSjb5HpPMCTQM+QFfdCipu9b223TNK+tyZinLjiiaC6HX5qBQW1zrnpwxjuKeFdO9BUETPwhOs5QCG/9dDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:45.725474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07388","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e8aeb1646f5bbf7235c7629153c2b7731d9da0191f4af260d3c4c5e901d9f72","sha256:090d55fd912872b87118847241796655ce4af6b45adb2a8217790a96f835dd57"],"state_sha256":"5c6aa0f627398d583fc73e5067f836bf878be35acea46a8bbf895d8dc7f3ef5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxjANndmMY9l+TOBewHsX2yi9GPzCfnAHJduacDzrtbNsNUZcok3i3PUy+JSjKDaDlWLWO1EguIw5XyOn6rjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:18:29.515494Z","bundle_sha256":"6d5e75e3cd86a636a8be27c2e041ab7e73c422470f9c725ecaf8052901434d98"}}