{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:F7YBU33TQJ7FXVTKLCWVBAYGUG","short_pith_number":"pith:F7YBU33T","canonical_record":{"source":{"id":"2606.08789","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-07T19:12:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ac559105d01b4307d2938d79717c6da74d5f5d1b09eb9b54d28df45161042646","abstract_canon_sha256":"857606279b5130cef973b122754e434fba6c314275f04a0ee470812da3e25365"},"schema_version":"1.0"},"canonical_sha256":"2ff01a6f73827e5bd66a58ad508306a1a2c46048799052c27c0ba06f5bd7eb8c","source":{"kind":"arxiv","id":"2606.08789","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08789","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08789v1","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08789","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_12","alias_value":"F7YBU33TQJ7F","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_16","alias_value":"F7YBU33TQJ7FXVTK","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_8","alias_value":"F7YBU33T","created_at":"2026-06-09T02:07:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:F7YBU33TQJ7FXVTKLCWVBAYGUG","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08789","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-07T19:12:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ac559105d01b4307d2938d79717c6da74d5f5d1b09eb9b54d28df45161042646","abstract_canon_sha256":"857606279b5130cef973b122754e434fba6c314275f04a0ee470812da3e25365"},"schema_version":"1.0"},"canonical_sha256":"2ff01a6f73827e5bd66a58ad508306a1a2c46048799052c27c0ba06f5bd7eb8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:39.462816Z","signature_b64":"6YeI5f1FlRKN74VZOrVPnlipv/pZmOOJg9Tj/xYFssZN8mY9Ra4I1gqluFrkUO39qXa536E2jqhzP3a9o++ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff01a6f73827e5bd66a58ad508306a1a2c46048799052c27c0ba06f5bd7eb8c","last_reissued_at":"2026-06-09T02:07:39.461993Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:39.461993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08789","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":"2026-06-09T02:07:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K27FzTdLBj94LArBt4FfIJKx2XNOKG3m//t93L6Ue/+FJxxNFpUJ+Mrn3lTyFpF5xeLzo1tgYJ6XSXoAN3B9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:32:15.093104Z"},"content_sha256":"cc62e00c2a85759dac186f79e462e3395799e3a56f7afa7c68b111e9be51e426","schema_version":"1.0","event_id":"sha256:cc62e00c2a85759dac186f79e462e3395799e3a56f7afa7c68b111e9be51e426"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:F7YBU33TQJ7FXVTKLCWVBAYGUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elastodynamics from a variational standpoint: integral equalities and inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lev Truskinovsky, Yury Grabovsky","submitted_at":"2026-06-07T19:12:37Z","abstract_excerpt":"As it is well known, solutions of equations of nonlinear elastodynamics, representing extremals of the action functional, can form shocks. We adapt the classical approach of Emmy Noether to such singular extremals and derive the appropriately generalized integral relations within Calculus of Variations. We apply them to elastodynamical extremals with shocks, obtaining new integral relations involving kinetic and elastic energies. For the extremals representing thermodynamically admissible (entropy) solutions of the corresponding hyperbolic Euler-Lagrange equations, the classical equalities, ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08789","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/2606.08789/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":"2026-06-09T02:07:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyTSGVc3jUNpG2riXJMu4fIOrIkljBTDeWx0FGP4qoh48EoExwFLs8WCsdEIaM5BgH67M+XxYyJXlo0UcDxhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:32:15.093496Z"},"content_sha256":"69f4edcc29e876e2d5dc50c2b4e16ba2264c1180bdb0cd79e2aa2d495adcb135","schema_version":"1.0","event_id":"sha256:69f4edcc29e876e2d5dc50c2b4e16ba2264c1180bdb0cd79e2aa2d495adcb135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/bundle.json","state_url":"https://pith.science/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/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":"2026-06-26T19:32:15Z","links":{"resolver":"https://pith.science/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG","bundle":"https://pith.science/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/bundle.json","state":"https://pith.science/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7YBU33TQJ7FXVTKLCWVBAYGUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F7YBU33TQJ7FXVTKLCWVBAYGUG","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":"857606279b5130cef973b122754e434fba6c314275f04a0ee470812da3e25365","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-07T19:12:37Z","title_canon_sha256":"ac559105d01b4307d2938d79717c6da74d5f5d1b09eb9b54d28df45161042646"},"schema_version":"1.0","source":{"id":"2606.08789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08789","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08789v1","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08789","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_12","alias_value":"F7YBU33TQJ7F","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_16","alias_value":"F7YBU33TQJ7FXVTK","created_at":"2026-06-09T02:07:39Z"},{"alias_kind":"pith_short_8","alias_value":"F7YBU33T","created_at":"2026-06-09T02:07:39Z"}],"graph_snapshots":[{"event_id":"sha256:69f4edcc29e876e2d5dc50c2b4e16ba2264c1180bdb0cd79e2aa2d495adcb135","target":"graph","created_at":"2026-06-09T02:07:39Z","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/2606.08789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As it is well known, solutions of equations of nonlinear elastodynamics, representing extremals of the action functional, can form shocks. We adapt the classical approach of Emmy Noether to such singular extremals and derive the appropriately generalized integral relations within Calculus of Variations. We apply them to elastodynamical extremals with shocks, obtaining new integral relations involving kinetic and elastic energies. For the extremals representing thermodynamically admissible (entropy) solutions of the corresponding hyperbolic Euler-Lagrange equations, the classical equalities, ch","authors_text":"Lev Truskinovsky, Yury Grabovsky","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-07T19:12:37Z","title":"Elastodynamics from a variational standpoint: integral equalities and inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08789","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:cc62e00c2a85759dac186f79e462e3395799e3a56f7afa7c68b111e9be51e426","target":"record","created_at":"2026-06-09T02:07:39Z","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":"857606279b5130cef973b122754e434fba6c314275f04a0ee470812da3e25365","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-07T19:12:37Z","title_canon_sha256":"ac559105d01b4307d2938d79717c6da74d5f5d1b09eb9b54d28df45161042646"},"schema_version":"1.0","source":{"id":"2606.08789","kind":"arxiv","version":1}},"canonical_sha256":"2ff01a6f73827e5bd66a58ad508306a1a2c46048799052c27c0ba06f5bd7eb8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff01a6f73827e5bd66a58ad508306a1a2c46048799052c27c0ba06f5bd7eb8c","first_computed_at":"2026-06-09T02:07:39.461993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:39.461993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6YeI5f1FlRKN74VZOrVPnlipv/pZmOOJg9Tj/xYFssZN8mY9Ra4I1gqluFrkUO39qXa536E2jqhzP3a9o++ZBw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:39.462816Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc62e00c2a85759dac186f79e462e3395799e3a56f7afa7c68b111e9be51e426","sha256:69f4edcc29e876e2d5dc50c2b4e16ba2264c1180bdb0cd79e2aa2d495adcb135"],"state_sha256":"c441930b59ee5db1b68283f930c0c08522f66aca5ec09447359da33bccd8ff11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlI5BnbJZVzQ0dc6fbFvQySsrG4dtn8xtOY01Frw6Od1ErhACkKlhkEOHxfZdCSbXjLV9y+o3Bh9QP3QG0c0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T19:32:15.096150Z","bundle_sha256":"7475e6d12b927e7ab90a36d3cd9033c12907d6e4403fc57b9403e26b58767d5a"}}