{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:G6ZL6FZXXW72ZL3QYPHRLER22D","short_pith_number":"pith:G6ZL6FZX","canonical_record":{"source":{"id":"1508.07765","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T11:10:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"32ade116762215c6c56ba23761e82c4bb2a8137641a6ba2556c58eaece53e6d6","abstract_canon_sha256":"c76fb35476caa394022ee9edc18e5663cc651595e5e078ecae882134c49c0c2e"},"schema_version":"1.0"},"canonical_sha256":"37b2bf1737bdbfacaf70c3cf15923ad0e303cfaab37e3090c50c1aaf52e04b36","source":{"kind":"arxiv","id":"1508.07765","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07765","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07765v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07765","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"G6ZL6FZXXW72","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G6ZL6FZXXW72ZL3Q","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G6ZL6FZX","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:G6ZL6FZXXW72ZL3QYPHRLER22D","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07765","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T11:10:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"32ade116762215c6c56ba23761e82c4bb2a8137641a6ba2556c58eaece53e6d6","abstract_canon_sha256":"c76fb35476caa394022ee9edc18e5663cc651595e5e078ecae882134c49c0c2e"},"schema_version":"1.0"},"canonical_sha256":"37b2bf1737bdbfacaf70c3cf15923ad0e303cfaab37e3090c50c1aaf52e04b36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.300306Z","signature_b64":"ERNBOBv3pTOM8eTp3n+6uvf0eirCr3QfeouGsvu3coLIbRR+oGOVUhLbllfizXk8e7qmBtrD7ZcvzwRsNADbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37b2bf1737bdbfacaf70c3cf15923ad0e303cfaab37e3090c50c1aaf52e04b36","last_reissued_at":"2026-05-18T00:52:02.299697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.299697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07765","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XZe06EYI+JkuvM59JSb5f7GQ4cILEUQBgKpHscZv6tD+5APB/lFNdj+dNSFVCLJ1OsLFaZQRxOaq7QrE4MmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:38:18.794550Z"},"content_sha256":"c266ec0628bd4edefa38fc331cf52bf2168d13890bba7dd5a4c843cb0759f95a","schema_version":"1.0","event_id":"sha256:c266ec0628bd4edefa38fc331cf52bf2168d13890bba7dd5a4c843cb0759f95a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:G6ZL6FZXXW72ZL3QYPHRLER22D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curved space-times by crystallization of liquid fiber bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dimitri Vey, Fr\\'ed\\'eric H\\'elein","submitted_at":"2015-08-31T11:10:16Z","abstract_excerpt":"Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of $((\\alpha,\\omega),\\varpi)$, where $(\\alpha,\\omega)$ is a 1-form with coefficients in the Lie algebra of the Poincar\\'e group and $\\varpi$ is an 8-form with coefficients in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07765","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6OrKweln9TCkSEG0zCqopO5QcOwozUpQeUEgffqvUNpDYQlL+JQAgvIrCMsAGoQhHOB+jNXS16LjJw2BbNtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:38:18.794910Z"},"content_sha256":"c4ee494a854421682d1d53cfdf86c995eee2edb6dbf6eaad4ca25b73ffa440ba","schema_version":"1.0","event_id":"sha256:c4ee494a854421682d1d53cfdf86c995eee2edb6dbf6eaad4ca25b73ffa440ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/bundle.json","state_url":"https://pith.science/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/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":"2026-06-05T20:38:18Z","links":{"resolver":"https://pith.science/pith/G6ZL6FZXXW72ZL3QYPHRLER22D","bundle":"https://pith.science/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/bundle.json","state":"https://pith.science/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6ZL6FZXXW72ZL3QYPHRLER22D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G6ZL6FZXXW72ZL3QYPHRLER22D","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":"c76fb35476caa394022ee9edc18e5663cc651595e5e078ecae882134c49c0c2e","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T11:10:16Z","title_canon_sha256":"32ade116762215c6c56ba23761e82c4bb2a8137641a6ba2556c58eaece53e6d6"},"schema_version":"1.0","source":{"id":"1508.07765","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07765","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07765v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07765","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"G6ZL6FZXXW72","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G6ZL6FZXXW72ZL3Q","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G6ZL6FZX","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:c4ee494a854421682d1d53cfdf86c995eee2edb6dbf6eaad4ca25b73ffa440ba","target":"graph","created_at":"2026-05-18T00:52:02Z","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":"Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of $((\\alpha,\\omega),\\varpi)$, where $(\\alpha,\\omega)$ is a 1-form with coefficients in the Lie algebra of the Poincar\\'e group and $\\varpi$ is an 8-form with coefficients in the ","authors_text":"Dimitri Vey, Fr\\'ed\\'eric H\\'elein","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T11:10:16Z","title":"Curved space-times by crystallization of liquid fiber bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07765","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:c266ec0628bd4edefa38fc331cf52bf2168d13890bba7dd5a4c843cb0759f95a","target":"record","created_at":"2026-05-18T00:52:02Z","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":"c76fb35476caa394022ee9edc18e5663cc651595e5e078ecae882134c49c0c2e","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2015-08-31T11:10:16Z","title_canon_sha256":"32ade116762215c6c56ba23761e82c4bb2a8137641a6ba2556c58eaece53e6d6"},"schema_version":"1.0","source":{"id":"1508.07765","kind":"arxiv","version":2}},"canonical_sha256":"37b2bf1737bdbfacaf70c3cf15923ad0e303cfaab37e3090c50c1aaf52e04b36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37b2bf1737bdbfacaf70c3cf15923ad0e303cfaab37e3090c50c1aaf52e04b36","first_computed_at":"2026-05-18T00:52:02.299697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.299697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERNBOBv3pTOM8eTp3n+6uvf0eirCr3QfeouGsvu3coLIbRR+oGOVUhLbllfizXk8e7qmBtrD7ZcvzwRsNADbAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.300306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07765","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c266ec0628bd4edefa38fc331cf52bf2168d13890bba7dd5a4c843cb0759f95a","sha256:c4ee494a854421682d1d53cfdf86c995eee2edb6dbf6eaad4ca25b73ffa440ba"],"state_sha256":"e4589c904341665d2dcd3c0130ec99def65b159cbced61c0243fcc922f9c4899"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"woKdaqBpKMCWb15v4rUjd+zb7npc6loPPf9TMUWiLQ3cbbCpMRvgCpxUQsOb3ZDp339LnH+fGSxOxtJAN+HpDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:38:18.797655Z","bundle_sha256":"85d1c1401f7331034a4c769e1b002166a88c878dff302c016a51ee6fc539c5ab"}}