{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:N6VR33R27Y6YGDDCEWM2QOIJYW","short_pith_number":"pith:N6VR33R2","canonical_record":{"source":{"id":"2509.23600","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-09-28T03:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"5790f961a3ae90e23e93dd2765a3a60a792dd32e3d5c4c8d0222fac454b148a0","abstract_canon_sha256":"e56fd0729cec736f0449743dc1405d00cddb7ad2d239d391f5537cf15956b39e"},"schema_version":"1.0"},"canonical_sha256":"6fab1dee3afe3d830c622599a83909c5825d9735581001342b19575fd9ced92b","source":{"kind":"arxiv","id":"2509.23600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.23600","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2509.23600v1","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.23600","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"N6VR33R27Y6Y","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"N6VR33R27Y6YGDDC","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"N6VR33R2","created_at":"2026-07-02T00:18:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:N6VR33R27Y6YGDDCEWM2QOIJYW","target":"record","payload":{"canonical_record":{"source":{"id":"2509.23600","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-09-28T03:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"5790f961a3ae90e23e93dd2765a3a60a792dd32e3d5c4c8d0222fac454b148a0","abstract_canon_sha256":"e56fd0729cec736f0449743dc1405d00cddb7ad2d239d391f5537cf15956b39e"},"schema_version":"1.0"},"canonical_sha256":"6fab1dee3afe3d830c622599a83909c5825d9735581001342b19575fd9ced92b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:25.231274Z","signature_b64":"wk+RfI23Y6EB55oSn8zRU0phLTr/Gc3UBCV0cLEQEq4LHtRhioGfnz21gngmTxiguhJWaE69Xr0W0iItJsDcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fab1dee3afe3d830c622599a83909c5825d9735581001342b19575fd9ced92b","last_reissued_at":"2026-07-02T00:18:25.230601Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:25.230601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.23600","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":"2026-07-02T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZ3JfbIdx5OZogEYkZ7VCMhlkFL8fcZPVxHnQ+4BvM+ikbPUK6nusCGmOLVwzj4s6kiTz+wHUrv2YwdOpEolAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:25:38.249168Z"},"content_sha256":"7f478eb4ec6ded2fe3b77a5b3b4a48c19ccb0f58f5c9b9f4a7b2f3062333e306","schema_version":"1.0","event_id":"sha256:7f478eb4ec6ded2fe3b77a5b3b4a48c19ccb0f58f5c9b9f4a7b2f3062333e306"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:N6VR33R27Y6YGDDCEWM2QOIJYW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesic deviation to all orders via a tangent bundle formalism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Joon-Hwi Kim","submitted_at":"2025-09-28T03:09:14Z","abstract_excerpt":"We establish an in-in formalism for geodesic deviation as an alternative to Synge calculus, based on a covariant calculus of differential forms in tangent bundle. This derives the exact Lagrangian and equations governing the finite geodesic deviation between a free-falling test particle and an arbitrary observer, in terms of infinite sums whose coefficients are products of binomial coefficients. Explicit expressions are provided up to tenth order, finding agreements with the previous fourth-order result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.23600","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/2509.23600/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":"2026-07-02T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ucxxkrHLdRaHVsaW3g7p8P4QwzeV0RT/mFDXaGZs8yk1dFozr+3/y82gGQde7GAjK9tBQGkRyz9wvQVmgfs8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:25:38.249649Z"},"content_sha256":"a181543dfde520ae288c414b1d5c4482e48fef34fa1b1b1dd14c4a4c85674fc2","schema_version":"1.0","event_id":"sha256:a181543dfde520ae288c414b1d5c4482e48fef34fa1b1b1dd14c4a4c85674fc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/bundle.json","state_url":"https://pith.science/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/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":"2026-08-04T20:25:38Z","links":{"resolver":"https://pith.science/pith/N6VR33R27Y6YGDDCEWM2QOIJYW","bundle":"https://pith.science/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/bundle.json","state":"https://pith.science/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6VR33R27Y6YGDDCEWM2QOIJYW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:N6VR33R27Y6YGDDCEWM2QOIJYW","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":"e56fd0729cec736f0449743dc1405d00cddb7ad2d239d391f5537cf15956b39e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-09-28T03:09:14Z","title_canon_sha256":"5790f961a3ae90e23e93dd2765a3a60a792dd32e3d5c4c8d0222fac454b148a0"},"schema_version":"1.0","source":{"id":"2509.23600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.23600","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2509.23600v1","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.23600","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"N6VR33R27Y6Y","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"N6VR33R27Y6YGDDC","created_at":"2026-07-02T00:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"N6VR33R2","created_at":"2026-07-02T00:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:a181543dfde520ae288c414b1d5c4482e48fef34fa1b1b1dd14c4a4c85674fc2","target":"graph","created_at":"2026-07-02T00:18:25Z","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/2509.23600/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an in-in formalism for geodesic deviation as an alternative to Synge calculus, based on a covariant calculus of differential forms in tangent bundle. This derives the exact Lagrangian and equations governing the finite geodesic deviation between a free-falling test particle and an arbitrary observer, in terms of infinite sums whose coefficients are products of binomial coefficients. Explicit expressions are provided up to tenth order, finding agreements with the previous fourth-order result.","authors_text":"Joon-Hwi Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-09-28T03:09:14Z","title":"Geodesic deviation to all orders via a tangent bundle formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.23600","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":"sha256:7f478eb4ec6ded2fe3b77a5b3b4a48c19ccb0f58f5c9b9f4a7b2f3062333e306","target":"record","created_at":"2026-07-02T00:18:25Z","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":"e56fd0729cec736f0449743dc1405d00cddb7ad2d239d391f5537cf15956b39e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-09-28T03:09:14Z","title_canon_sha256":"5790f961a3ae90e23e93dd2765a3a60a792dd32e3d5c4c8d0222fac454b148a0"},"schema_version":"1.0","source":{"id":"2509.23600","kind":"arxiv","version":1}},"canonical_sha256":"6fab1dee3afe3d830c622599a83909c5825d9735581001342b19575fd9ced92b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fab1dee3afe3d830c622599a83909c5825d9735581001342b19575fd9ced92b","first_computed_at":"2026-07-02T00:18:25.230601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:25.230601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wk+RfI23Y6EB55oSn8zRU0phLTr/Gc3UBCV0cLEQEq4LHtRhioGfnz21gngmTxiguhJWaE69Xr0W0iItJsDcCA==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:25.231274Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.23600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f478eb4ec6ded2fe3b77a5b3b4a48c19ccb0f58f5c9b9f4a7b2f3062333e306","sha256:a181543dfde520ae288c414b1d5c4482e48fef34fa1b1b1dd14c4a4c85674fc2"],"state_sha256":"b541367496fbb48b9d0388d7aae5746964a1272dc95850aa0edee02595d1017f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55cUbdco/nsyMQXs0XDBg9AOccKgWonr/tR1RIxuy4THoVQsvXmZEfdD2l/YeiBoxXQB4BQv/1D1mUFI0wQsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:25:38.254361Z","bundle_sha256":"a8d303f15f6592f64d1506c008abb2bed68770e3e6b43c2e81c11e808f399f2f"}}