{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TIGEWJ6BY6K43YFGCXXWYVEW4Z","short_pith_number":"pith:TIGEWJ6B","canonical_record":{"source":{"id":"1602.00264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-31T15:43:16Z","cross_cats_sorted":[],"title_canon_sha256":"f3e3807f7b2897c495e5531a402bb20afd642668f7572316fdb36189e69262c7","abstract_canon_sha256":"183a6d7e808083bdf2e86221177ed902b568a9f550bba47b43d041c7c7fe4367"},"schema_version":"1.0"},"canonical_sha256":"9a0c4b27c1c795cde0a615ef6c5496e65de6f190fb6427e030b61ad22303415b","source":{"kind":"arxiv","id":"1602.00264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00264","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00264v1","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00264","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"pith_short_12","alias_value":"TIGEWJ6BY6K4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIGEWJ6BY6K43YFG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIGEWJ6B","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TIGEWJ6BY6K43YFGCXXWYVEW4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-31T15:43:16Z","cross_cats_sorted":[],"title_canon_sha256":"f3e3807f7b2897c495e5531a402bb20afd642668f7572316fdb36189e69262c7","abstract_canon_sha256":"183a6d7e808083bdf2e86221177ed902b568a9f550bba47b43d041c7c7fe4367"},"schema_version":"1.0"},"canonical_sha256":"9a0c4b27c1c795cde0a615ef6c5496e65de6f190fb6427e030b61ad22303415b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:35.850083Z","signature_b64":"KcD73toHosiyoyEZhFplD5XRnXYmDsYuXGP20+Tk3SzsnnUr0dSfefLTc4Nqd+et2dxUKow7GXX21BkyH4fEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a0c4b27c1c795cde0a615ef6c5496e65de6f190fb6427e030b61ad22303415b","last_reissued_at":"2026-05-18T01:21:35.849510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:35.849510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00264","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":"2026-05-18T01:21:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2vblkxq7Is8adawxLUzXkUuPglH1AkIfN6NU/vd95ghM6XAwUhTjvfj5RQe2vHdP5ITKPHJQPgGh7gWFDe2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:14:55.010516Z"},"content_sha256":"1cded068fc5fbf7723bab2a2f23cf3b1e90709a1ae82915c949f097eb75594ff","schema_version":"1.0","event_id":"sha256:1cded068fc5fbf7723bab2a2f23cf3b1e90709a1ae82915c949f097eb75594ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TIGEWJ6BY6K43YFGCXXWYVEW4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, weak solutions and the entropy condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edgardo P\\'erez, Krzysztof R\\'ozga","submitted_at":"2016-01-31T15:43:16Z","abstract_excerpt":"We consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a function $W$, called strain-energy function. We consider four forms of $W$ which are known in the literature. These are St.Venant-Kirchhoff, Ogden, Kirchhoff modified, Blatz-Ko-Ogden forms. In each of those cases we determine the conditions for the parameters $\\rho_0$, $\\mu $ and $\\lambda$, under which the corresponding system is hyperbolic and genuinely nonlinear. We also establish what it means a weak solution of an initial and boundary value problem. Next we concentr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00264","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":"2026-05-18T01:21:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoJ5qJw+Ljs9iOYg4DEGTimpb1klGg5J/k0O4RPAo0GhL4HvkKHbrMyH6lQLB6DwGH6NRGl7yz9Mi7WClXrNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:14:55.010862Z"},"content_sha256":"2d5e9938b5a6e18351a9f7b465f9e0b939190d438f6206cee65b113d9cc1327d","schema_version":"1.0","event_id":"sha256:2d5e9938b5a6e18351a9f7b465f9e0b939190d438f6206cee65b113d9cc1327d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/bundle.json","state_url":"https://pith.science/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/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":"2026-06-26T16:14:55Z","links":{"resolver":"https://pith.science/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z","bundle":"https://pith.science/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/bundle.json","state":"https://pith.science/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIGEWJ6BY6K43YFGCXXWYVEW4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIGEWJ6BY6K43YFGCXXWYVEW4Z","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":"183a6d7e808083bdf2e86221177ed902b568a9f550bba47b43d041c7c7fe4367","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-31T15:43:16Z","title_canon_sha256":"f3e3807f7b2897c495e5531a402bb20afd642668f7572316fdb36189e69262c7"},"schema_version":"1.0","source":{"id":"1602.00264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00264","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00264v1","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00264","created_at":"2026-05-18T01:21:35Z"},{"alias_kind":"pith_short_12","alias_value":"TIGEWJ6BY6K4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIGEWJ6BY6K43YFG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIGEWJ6B","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2d5e9938b5a6e18351a9f7b465f9e0b939190d438f6206cee65b113d9cc1327d","target":"graph","created_at":"2026-05-18T01:21:35Z","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 consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a function $W$, called strain-energy function. We consider four forms of $W$ which are known in the literature. These are St.Venant-Kirchhoff, Ogden, Kirchhoff modified, Blatz-Ko-Ogden forms. In each of those cases we determine the conditions for the parameters $\\rho_0$, $\\mu $ and $\\lambda$, under which the corresponding system is hyperbolic and genuinely nonlinear. We also establish what it means a weak solution of an initial and boundary value problem. Next we concentr","authors_text":"Edgardo P\\'erez, Krzysztof R\\'ozga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-31T15:43:16Z","title":"Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, weak solutions and the entropy condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00264","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":"sha256:1cded068fc5fbf7723bab2a2f23cf3b1e90709a1ae82915c949f097eb75594ff","target":"record","created_at":"2026-05-18T01:21:35Z","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":"183a6d7e808083bdf2e86221177ed902b568a9f550bba47b43d041c7c7fe4367","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-31T15:43:16Z","title_canon_sha256":"f3e3807f7b2897c495e5531a402bb20afd642668f7572316fdb36189e69262c7"},"schema_version":"1.0","source":{"id":"1602.00264","kind":"arxiv","version":1}},"canonical_sha256":"9a0c4b27c1c795cde0a615ef6c5496e65de6f190fb6427e030b61ad22303415b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a0c4b27c1c795cde0a615ef6c5496e65de6f190fb6427e030b61ad22303415b","first_computed_at":"2026-05-18T01:21:35.849510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:35.849510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KcD73toHosiyoyEZhFplD5XRnXYmDsYuXGP20+Tk3SzsnnUr0dSfefLTc4Nqd+et2dxUKow7GXX21BkyH4fEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:35.850083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cded068fc5fbf7723bab2a2f23cf3b1e90709a1ae82915c949f097eb75594ff","sha256:2d5e9938b5a6e18351a9f7b465f9e0b939190d438f6206cee65b113d9cc1327d"],"state_sha256":"a82874eda1e778a0e6de9b4f299c3e43b62cca1231cd0c73c467a941d2f585cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KwPPQTxKTB6DUJyRSVRm0jtiIqvlPm/67yo06JqanSJ7XdDj2avo889Q2+GLiqr2/T8OYM+gqQtx+wEboYJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:14:55.012875Z","bundle_sha256":"044bacef412fcac9ed0a40e3395658c3cd904d1484adfe20b4a57bf331e43b4a"}}