{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NFYNRMFGWI6UUYIGBYQZO4VC36","short_pith_number":"pith:NFYNRMFG","canonical_record":{"source":{"id":"1506.03814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-11T20:00:36Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"806b51e4c219dde928e62a37a8ec7561f833ddd040ef1bc2e66c286fe6517054","abstract_canon_sha256":"c7ac395eb276772ad7d7ffdcd05a82875dd94a57d19eb8a0d89d02195f905e61"},"schema_version":"1.0"},"canonical_sha256":"6970d8b0a6b23d4a61060e219772a2df95372cf313384331a0027ac688ba38ca","source":{"kind":"arxiv","id":"1506.03814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03814","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03814v1","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03814","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"NFYNRMFGWI6U","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFYNRMFGWI6UUYIG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFYNRMFG","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NFYNRMFGWI6UUYIGBYQZO4VC36","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-11T20:00:36Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"806b51e4c219dde928e62a37a8ec7561f833ddd040ef1bc2e66c286fe6517054","abstract_canon_sha256":"c7ac395eb276772ad7d7ffdcd05a82875dd94a57d19eb8a0d89d02195f905e61"},"schema_version":"1.0"},"canonical_sha256":"6970d8b0a6b23d4a61060e219772a2df95372cf313384331a0027ac688ba38ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:54.662086Z","signature_b64":"7fk4tQ4IHuwUKjiogQpyDJpmLylHK+lSFhJ7lceMV9BRFYMBB25scX3ADBwQ01cR1+RODYmwB8zf8eit7InNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6970d8b0a6b23d4a61060e219772a2df95372cf313384331a0027ac688ba38ca","last_reissued_at":"2026-05-18T01:24:54.661393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:54.661393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03814","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":"2026-05-18T01:24:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQv2tA4KtPTr8v7TsO7VqbkIVmdFEYwhxSKkAGJd+PfdoUOYZDhugJIEtffTdnaW4Pr5USlOz8GZbCGKwPwQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T14:10:21.374562Z"},"content_sha256":"51b393d756fe2b38748c34c9bfc5d529a89b79ecf87e6aa8efcdd30c1be151ea","schema_version":"1.0","event_id":"sha256:51b393d756fe2b38748c34c9bfc5d529a89b79ecf87e6aa8efcdd30c1be151ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NFYNRMFGWI6UUYIGBYQZO4VC36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Momentum density of spacetime and the gravitational dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"T. Padmanabhan","submitted_at":"2015-06-11T20:00:36Z","abstract_excerpt":"I introduce a covariant four-vector $\\mathcal{G}^a[v]$, which can be interpreted as the momentum density attributed to the spacetime geometry by an observer with velocity $v^a$, and describe its properties: (a) Demanding that the total momentum of matter plus geometry is conserved for all observers, leads to the gravitational field equations. Thus, how matter curves spacetime is entirely determined by this principle of momentum conservation. (b) The $\\mathcal{G}^a[v]$ can be related to the gravitational Lagrangian in a manner similar to the usual definition of Hamiltonian in, say, classical me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03814","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":"2026-05-18T01:24:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bpctUWL6P5H0CINSsm1SSAM0/VhPJxmwWjgFFo3irZK5SwvrsEY2u6MPrR3S79Jc9LjfT0PtUX/o6Pzw/pwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T14:10:21.374912Z"},"content_sha256":"b3853a6207917039d743911d0842dc3341a194f28939516d3ec363e85154283f","schema_version":"1.0","event_id":"sha256:b3853a6207917039d743911d0842dc3341a194f28939516d3ec363e85154283f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/bundle.json","state_url":"https://pith.science/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/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":"2026-07-11T14:10:21Z","links":{"resolver":"https://pith.science/pith/NFYNRMFGWI6UUYIGBYQZO4VC36","bundle":"https://pith.science/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/bundle.json","state":"https://pith.science/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFYNRMFGWI6UUYIGBYQZO4VC36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NFYNRMFGWI6UUYIGBYQZO4VC36","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":"c7ac395eb276772ad7d7ffdcd05a82875dd94a57d19eb8a0d89d02195f905e61","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-11T20:00:36Z","title_canon_sha256":"806b51e4c219dde928e62a37a8ec7561f833ddd040ef1bc2e66c286fe6517054"},"schema_version":"1.0","source":{"id":"1506.03814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03814","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03814v1","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03814","created_at":"2026-05-18T01:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"NFYNRMFGWI6U","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFYNRMFGWI6UUYIG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFYNRMFG","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:b3853a6207917039d743911d0842dc3341a194f28939516d3ec363e85154283f","target":"graph","created_at":"2026-05-18T01:24:54Z","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":"I introduce a covariant four-vector $\\mathcal{G}^a[v]$, which can be interpreted as the momentum density attributed to the spacetime geometry by an observer with velocity $v^a$, and describe its properties: (a) Demanding that the total momentum of matter plus geometry is conserved for all observers, leads to the gravitational field equations. Thus, how matter curves spacetime is entirely determined by this principle of momentum conservation. (b) The $\\mathcal{G}^a[v]$ can be related to the gravitational Lagrangian in a manner similar to the usual definition of Hamiltonian in, say, classical me","authors_text":"T. Padmanabhan","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-11T20:00:36Z","title":"Momentum density of spacetime and the gravitational dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03814","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":"sha256:51b393d756fe2b38748c34c9bfc5d529a89b79ecf87e6aa8efcdd30c1be151ea","target":"record","created_at":"2026-05-18T01:24:54Z","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":"c7ac395eb276772ad7d7ffdcd05a82875dd94a57d19eb8a0d89d02195f905e61","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-11T20:00:36Z","title_canon_sha256":"806b51e4c219dde928e62a37a8ec7561f833ddd040ef1bc2e66c286fe6517054"},"schema_version":"1.0","source":{"id":"1506.03814","kind":"arxiv","version":1}},"canonical_sha256":"6970d8b0a6b23d4a61060e219772a2df95372cf313384331a0027ac688ba38ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6970d8b0a6b23d4a61060e219772a2df95372cf313384331a0027ac688ba38ca","first_computed_at":"2026-05-18T01:24:54.661393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:54.661393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7fk4tQ4IHuwUKjiogQpyDJpmLylHK+lSFhJ7lceMV9BRFYMBB25scX3ADBwQ01cR1+RODYmwB8zf8eit7InNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:54.662086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51b393d756fe2b38748c34c9bfc5d529a89b79ecf87e6aa8efcdd30c1be151ea","sha256:b3853a6207917039d743911d0842dc3341a194f28939516d3ec363e85154283f"],"state_sha256":"a0abb95777928acba36d282cb277d114ba85e6e1ba7bb5a4628a1f9b994cf15a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nBhxjXKN9NhxeefQmPSZ56UGpBcFSbawyANcNrVf2hQKN5nwEnG5+/DurPElxUtAWA5/kUZTiNzuOLyVlj1eCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T14:10:21.376988Z","bundle_sha256":"b42ea18f8f6390e5b97b540cfc47350363db403cc940be12989a0d33c4f935fb"}}