{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:QX3QHL6SCCHHJDVT62WGBIFCEO","short_pith_number":"pith:QX3QHL6S","canonical_record":{"source":{"id":"gr-qc/0403094","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-03-23T13:37:01Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"8de7a133735a7b888efcc308f6a65ed8d73fe85cf88ae5d36eda9fbf08fa495b","abstract_canon_sha256":"7c07fb2bfd6ab76e23a18031b5e19311e71ec617de415286c3c72313e2344575"},"schema_version":"1.0"},"canonical_sha256":"85f703afd2108e748eb3f6ac60a0a223b86aae4af160d0329bfd819aba0598a3","source":{"kind":"arxiv","id":"gr-qc/0403094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0403094","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0403094v2","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0403094","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"QX3QHL6SCCHH","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_16","alias_value":"QX3QHL6SCCHHJDVT","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_8","alias_value":"QX3QHL6S","created_at":"2026-07-04T16:47:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:QX3QHL6SCCHHJDVT62WGBIFCEO","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0403094","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-03-23T13:37:01Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"8de7a133735a7b888efcc308f6a65ed8d73fe85cf88ae5d36eda9fbf08fa495b","abstract_canon_sha256":"7c07fb2bfd6ab76e23a18031b5e19311e71ec617de415286c3c72313e2344575"},"schema_version":"1.0"},"canonical_sha256":"85f703afd2108e748eb3f6ac60a0a223b86aae4af160d0329bfd819aba0598a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:47:42.606230Z","signature_b64":"6SjSKQOhLSlXhvVWPLV5JIbyU6JgkJf4M9PC2dKmRkXGNA8++Cw1b1ct0vRrKtvH6WKHeHFdJ6zT16kmIVrUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f703afd2108e748eb3f6ac60a0a223b86aae4af160d0329bfd819aba0598a3","last_reissued_at":"2026-07-04T16:47:42.605867Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:47:42.605867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0403094","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":"2026-07-04T16:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bClawbS0aHoSgtnoI/H9YwaKlVC9fJGwWFD+dTecSxQwaPSHuv/JO9cmuhDVla4DZhakqpRxcgYMYLfFkl8FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:24:32.758935Z"},"content_sha256":"9381761a5e9e37a44d38bee666f24a538b5b64023fec76befaa19a336ea08b63","schema_version":"1.0","event_id":"sha256:9381761a5e9e37a44d38bee666f24a538b5b64023fec76befaa19a336ea08b63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:QX3QHL6SCCHHJDVT62WGBIFCEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"World function and time transfer: general post-Minkowskian expansions","license":"","headline":"","cross_cats":["astro-ph"],"primary_cat":"gr-qc","authors_text":"Bernard Linet, Christophe Le Poncin-lafitte, Pierre Teyssandier","submitted_at":"2004-03-23T13:37:01Z","abstract_excerpt":"In suitably chosen domains of space-time, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian gravitational constant G. We show rigorously that each perturbation term is given by a line integral taken along the unperturbed geodesic between two points. Once the world function is known, it becomes possible to determine the time transfer functions giving the propagation time of a photon between"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0403094","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/0403094/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":"2026-07-04T16:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOpi25mYnjrIGrKWjv4hpEeupme1o1hzi6fHNsbtpPztxdUWrLzv/pZeiTCFVFeePWZvNopwAB97+dk+WzQfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:24:32.759452Z"},"content_sha256":"2fb3e7307c542bb420af0819fd31da1dfbdb139714a39d57bd78a5fff1758b71","schema_version":"1.0","event_id":"sha256:2fb3e7307c542bb420af0819fd31da1dfbdb139714a39d57bd78a5fff1758b71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/bundle.json","state_url":"https://pith.science/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/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":"2026-08-08T06:24:32Z","links":{"resolver":"https://pith.science/pith/QX3QHL6SCCHHJDVT62WGBIFCEO","bundle":"https://pith.science/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/bundle.json","state":"https://pith.science/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QX3QHL6SCCHHJDVT62WGBIFCEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:QX3QHL6SCCHHJDVT62WGBIFCEO","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":"7c07fb2bfd6ab76e23a18031b5e19311e71ec617de415286c3c72313e2344575","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-03-23T13:37:01Z","title_canon_sha256":"8de7a133735a7b888efcc308f6a65ed8d73fe85cf88ae5d36eda9fbf08fa495b"},"schema_version":"1.0","source":{"id":"gr-qc/0403094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0403094","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0403094v2","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0403094","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"QX3QHL6SCCHH","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_16","alias_value":"QX3QHL6SCCHHJDVT","created_at":"2026-07-04T16:47:42Z"},{"alias_kind":"pith_short_8","alias_value":"QX3QHL6S","created_at":"2026-07-04T16:47:42Z"}],"graph_snapshots":[{"event_id":"sha256:2fb3e7307c542bb420af0819fd31da1dfbdb139714a39d57bd78a5fff1758b71","target":"graph","created_at":"2026-07-04T16:47:42Z","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/gr-qc/0403094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In suitably chosen domains of space-time, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian gravitational constant G. We show rigorously that each perturbation term is given by a line integral taken along the unperturbed geodesic between two points. Once the world function is known, it becomes possible to determine the time transfer functions giving the propagation time of a photon between","authors_text":"Bernard Linet, Christophe Le Poncin-lafitte, Pierre Teyssandier","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2004-03-23T13:37:01Z","title":"World function and time transfer: general post-Minkowskian expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0403094","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":"sha256:9381761a5e9e37a44d38bee666f24a538b5b64023fec76befaa19a336ea08b63","target":"record","created_at":"2026-07-04T16:47:42Z","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":"7c07fb2bfd6ab76e23a18031b5e19311e71ec617de415286c3c72313e2344575","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-03-23T13:37:01Z","title_canon_sha256":"8de7a133735a7b888efcc308f6a65ed8d73fe85cf88ae5d36eda9fbf08fa495b"},"schema_version":"1.0","source":{"id":"gr-qc/0403094","kind":"arxiv","version":2}},"canonical_sha256":"85f703afd2108e748eb3f6ac60a0a223b86aae4af160d0329bfd819aba0598a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f703afd2108e748eb3f6ac60a0a223b86aae4af160d0329bfd819aba0598a3","first_computed_at":"2026-07-04T16:47:42.605867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:47:42.605867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6SjSKQOhLSlXhvVWPLV5JIbyU6JgkJf4M9PC2dKmRkXGNA8++Cw1b1ct0vRrKtvH6WKHeHFdJ6zT16kmIVrUBw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:47:42.606230Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0403094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9381761a5e9e37a44d38bee666f24a538b5b64023fec76befaa19a336ea08b63","sha256:2fb3e7307c542bb420af0819fd31da1dfbdb139714a39d57bd78a5fff1758b71"],"state_sha256":"08dcc4bba913fa7e45532501b65615d2debed30b8edd33a00023574fd596d329"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ft1fbXa15Ro+LCIWnDFsPzuPV7p3Zvkfl6XaM/t+DTohhDjATnHFYSkEMSbHLBlAfST/mBrItzB6EXoROlm2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T06:24:32.763985Z","bundle_sha256":"cb910a41e1dbda38a6a67e98167f191eb0e14b786e33be92edfcbdab0db71e65"}}