{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:33BKVLCB2XHPL3LKQWUORUFNUX","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":"20f34ee1eebbce31590bb7f55725ee43ebc374504bd2d77e82cde86b27918792","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-27T17:24:19Z","title_canon_sha256":"bac2ad4a05819642a8101216c0bbb9a6ade20aa02c0baa73ff67bd462ce051de"},"schema_version":"1.0","source":{"id":"1906.11805","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11805","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11805v2","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11805","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"33BKVLCB2XHP","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_16","alias_value":"33BKVLCB2XHPL3LK","created_at":"2026-07-05T00:22:40Z"},{"alias_kind":"pith_short_8","alias_value":"33BKVLCB","created_at":"2026-07-05T00:22:40Z"}],"graph_snapshots":[{"event_id":"sha256:09bc880126064b5f2b5915caa5357ef161d36c32eaa0adf1afad851ab4b3e744","target":"graph","created_at":"2026-07-05T00:22:40Z","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/1906.11805/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The piecewise flat spacetime is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine-connection form of the Regge action of our previous work, we get a second order form of the action. This can be expanded over metric variations from simplex ","authors_text":"V.M. Khatsymovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-27T17:24:19Z","title":"On the discrete Christoffel symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11805","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":"sha256:845a664ad4be2dfc8e304441aba461c9b90e660988dbdd025ea7858a64d2faa0","target":"record","created_at":"2026-07-05T00:22:40Z","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":"20f34ee1eebbce31590bb7f55725ee43ebc374504bd2d77e82cde86b27918792","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-27T17:24:19Z","title_canon_sha256":"bac2ad4a05819642a8101216c0bbb9a6ade20aa02c0baa73ff67bd462ce051de"},"schema_version":"1.0","source":{"id":"1906.11805","kind":"arxiv","version":2}},"canonical_sha256":"dec2aaac41d5cef5ed6a85a8e8d0ada5c1d0e654805bb3db2644082af13c1c9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dec2aaac41d5cef5ed6a85a8e8d0ada5c1d0e654805bb3db2644082af13c1c9a","first_computed_at":"2026-07-05T00:22:40.380310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:40.380310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Te7DIEwxtUwICRXG4qklKdmYXi1sumruYoAjHO0JSBAUlRKS936ezYpEiDKZj5x5/9hyH6nx4kdb4NHvDCwCDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:40.380825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11805","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:845a664ad4be2dfc8e304441aba461c9b90e660988dbdd025ea7858a64d2faa0","sha256:09bc880126064b5f2b5915caa5357ef161d36c32eaa0adf1afad851ab4b3e744"],"state_sha256":"812a04e2967e0bbf09d1b9e698fc6a33ed3382f83773bc0fff255ddcc5659768"}