{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JK46KUTCWQ42G74CREFSLNNLHP","short_pith_number":"pith:JK46KUTC","canonical_record":{"source":{"id":"2507.13030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-07-17T11:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"f891e6d58a2c7bf8c6eeab2d877c3d3d261d79e6d7b80e55e5463b847adbc2fd","abstract_canon_sha256":"6c81d0bbfcf33a7ea6198a6d3c8e8eb9a2c7f3de36ab8846af9f84eb9a37ba90"},"schema_version":"1.0"},"canonical_sha256":"4ab9e55262b439a37f82890b25b5ab3bfd6c3edd1bc8fc8471d5d7a40bd97019","source":{"kind":"arxiv","id":"2507.13030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13030","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13030v1","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13030","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"JK46KUTCWQ42","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"JK46KUTCWQ42G74C","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"JK46KUTC","created_at":"2026-07-05T11:38:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JK46KUTCWQ42G74CREFSLNNLHP","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-07-17T11:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"f891e6d58a2c7bf8c6eeab2d877c3d3d261d79e6d7b80e55e5463b847adbc2fd","abstract_canon_sha256":"6c81d0bbfcf33a7ea6198a6d3c8e8eb9a2c7f3de36ab8846af9f84eb9a37ba90"},"schema_version":"1.0"},"canonical_sha256":"4ab9e55262b439a37f82890b25b5ab3bfd6c3edd1bc8fc8471d5d7a40bd97019","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:53.369447Z","signature_b64":"wB9RJx9QfznxvvEJ4Rz3N2WAUG98oRcEOiNzKB9WPY30OczWhn7KBNPh7KFdBKQbCxHsR1nxIhOFIgCl/e9bAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ab9e55262b439a37f82890b25b5ab3bfd6c3edd1bc8fc8471d5d7a40bd97019","last_reissued_at":"2026-07-05T11:38:53.369008Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:53.369008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13030","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":"2026-07-05T11:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVHqWIsi+IFelLNVut4FpkntTrKn/tJuBNaofHeQ37Y7XCXrIp6cHQTiKkPRPRFw2yG7neCByLkXM+dKbUK5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:06:55.291970Z"},"content_sha256":"702f47a93c3edc00b6a595fb65b5bda984c3fc69c8577b439e2c2542d86e50af","schema_version":"1.0","event_id":"sha256:702f47a93c3edc00b6a595fb65b5bda984c3fc69c8577b439e2c2542d86e50af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JK46KUTCWQ42G74CREFSLNNLHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relativistic second gradient theory of continuous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Boris Kolev (LMPS), Cl\\'ement Ecker (LMPS), Lionel Darondeau (IMJ-PRG), LMPS), Mina Chapon (LMPS), Rodrigue Desmorat (LMT","submitted_at":"2025-07-17T11:59:41Z","abstract_excerpt":"Variational Relativity is a framework developed by Souriau in the sixties to better formulate General Relativity and its classical limit\\,: Classical Continuum Mechanics. It has been used, for instance, to formulate Hyperelasticity in General Relativity. In that case, two primary variables are involved, the universe (Lorentzian) metric $g$ and the matter field $\\Psi$. A Lagrangian density depending on the 1-jet of these variables is then introduced which must satisfy the principle of General Covariance. Souriau proved in 1958 that under these hypotheses, the Lagrangian density depends only on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13030","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/2507.13030/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":"2026-07-05T11:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+7oOV7SIAHvRMtNUFk1/nKVj8KCSlQlMG18j4CZRG9Tp6sqpG+q4MXZzeO99r+memKOi0E1Kw44/xnTcwfGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:06:55.292634Z"},"content_sha256":"6d987feb462c8b22c020f77810b1ea7cf06d40f2035b259653dc0c4bebbddd4d","schema_version":"1.0","event_id":"sha256:6d987feb462c8b22c020f77810b1ea7cf06d40f2035b259653dc0c4bebbddd4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JK46KUTCWQ42G74CREFSLNNLHP/bundle.json","state_url":"https://pith.science/pith/JK46KUTCWQ42G74CREFSLNNLHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JK46KUTCWQ42G74CREFSLNNLHP/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":"2026-08-12T20:06:55Z","links":{"resolver":"https://pith.science/pith/JK46KUTCWQ42G74CREFSLNNLHP","bundle":"https://pith.science/pith/JK46KUTCWQ42G74CREFSLNNLHP/bundle.json","state":"https://pith.science/pith/JK46KUTCWQ42G74CREFSLNNLHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JK46KUTCWQ42G74CREFSLNNLHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JK46KUTCWQ42G74CREFSLNNLHP","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":"6c81d0bbfcf33a7ea6198a6d3c8e8eb9a2c7f3de36ab8846af9f84eb9a37ba90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-07-17T11:59:41Z","title_canon_sha256":"f891e6d58a2c7bf8c6eeab2d877c3d3d261d79e6d7b80e55e5463b847adbc2fd"},"schema_version":"1.0","source":{"id":"2507.13030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13030","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13030v1","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13030","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"JK46KUTCWQ42","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"JK46KUTCWQ42G74C","created_at":"2026-07-05T11:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"JK46KUTC","created_at":"2026-07-05T11:38:53Z"}],"graph_snapshots":[{"event_id":"sha256:6d987feb462c8b22c020f77810b1ea7cf06d40f2035b259653dc0c4bebbddd4d","target":"graph","created_at":"2026-07-05T11:38:53Z","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/2507.13030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variational Relativity is a framework developed by Souriau in the sixties to better formulate General Relativity and its classical limit\\,: Classical Continuum Mechanics. It has been used, for instance, to formulate Hyperelasticity in General Relativity. In that case, two primary variables are involved, the universe (Lorentzian) metric $g$ and the matter field $\\Psi$. A Lagrangian density depending on the 1-jet of these variables is then introduced which must satisfy the principle of General Covariance. Souriau proved in 1958 that under these hypotheses, the Lagrangian density depends only on ","authors_text":"Boris Kolev (LMPS), Cl\\'ement Ecker (LMPS), Lionel Darondeau (IMJ-PRG), LMPS), Mina Chapon (LMPS), Rodrigue Desmorat (LMT","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-07-17T11:59:41Z","title":"Relativistic second gradient theory of continuous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13030","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":"sha256:702f47a93c3edc00b6a595fb65b5bda984c3fc69c8577b439e2c2542d86e50af","target":"record","created_at":"2026-07-05T11:38:53Z","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":"6c81d0bbfcf33a7ea6198a6d3c8e8eb9a2c7f3de36ab8846af9f84eb9a37ba90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-07-17T11:59:41Z","title_canon_sha256":"f891e6d58a2c7bf8c6eeab2d877c3d3d261d79e6d7b80e55e5463b847adbc2fd"},"schema_version":"1.0","source":{"id":"2507.13030","kind":"arxiv","version":1}},"canonical_sha256":"4ab9e55262b439a37f82890b25b5ab3bfd6c3edd1bc8fc8471d5d7a40bd97019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ab9e55262b439a37f82890b25b5ab3bfd6c3edd1bc8fc8471d5d7a40bd97019","first_computed_at":"2026-07-05T11:38:53.369008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:53.369008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wB9RJx9QfznxvvEJ4Rz3N2WAUG98oRcEOiNzKB9WPY30OczWhn7KBNPh7KFdBKQbCxHsR1nxIhOFIgCl/e9bAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:53.369447Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:702f47a93c3edc00b6a595fb65b5bda984c3fc69c8577b439e2c2542d86e50af","sha256:6d987feb462c8b22c020f77810b1ea7cf06d40f2035b259653dc0c4bebbddd4d"],"state_sha256":"b7da13cd3979f79dc6c29b0b63b7d8b584912ef3f37ac3de9544b4a6e6e7e25c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"we6uFQSQigz+u0Vd/7J8TunlkbhK/JNBswxsP5IqljEOBHk+z1XmM0LJiOsrga1YF3q3xvwJFfabJJyJoMlCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:06:55.297437Z","bundle_sha256":"30025567fc3fe5f924141ae4fa5ec98ed503aaa8ac03b129951ed2d58d2f6288"}}