{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:73VUO7QH2PTZQDKBKMCXN32KUO","short_pith_number":"pith:73VUO7QH","canonical_record":{"source":{"id":"2107.04903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-07-10T20:18:02Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"fb8c9bd3c316d7fab9b01e471f8fe07af1949a34a8344f7664f14808ef452069","abstract_canon_sha256":"d4a5097660787414578ec679fdd61394f11bd799219598dda59864bc3d655682"},"schema_version":"1.0"},"canonical_sha256":"feeb477e07d3e7980d41530576ef4aa39061c50e93f9987978a14c5ff7d2e4bf","source":{"kind":"arxiv","id":"2107.04903","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.04903","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2107.04903v2","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04903","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"73VUO7QH2PTZ","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"73VUO7QH2PTZQDKB","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"73VUO7QH","created_at":"2026-07-05T03:21:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:73VUO7QH2PTZQDKBKMCXN32KUO","target":"record","payload":{"canonical_record":{"source":{"id":"2107.04903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-07-10T20:18:02Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"fb8c9bd3c316d7fab9b01e471f8fe07af1949a34a8344f7664f14808ef452069","abstract_canon_sha256":"d4a5097660787414578ec679fdd61394f11bd799219598dda59864bc3d655682"},"schema_version":"1.0"},"canonical_sha256":"feeb477e07d3e7980d41530576ef4aa39061c50e93f9987978a14c5ff7d2e4bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:21:12.457238Z","signature_b64":"7F/OJ1hDfQCijFj1J+1QvKvA+sjfP922wvCCQEg20N/D3EHHdBsImRy8++4Q64y5qo62MdLstAhpfV92EeI3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feeb477e07d3e7980d41530576ef4aa39061c50e93f9987978a14c5ff7d2e4bf","last_reissued_at":"2026-07-05T03:21:12.456763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:21:12.456763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.04903","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":"2026-07-05T03:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7bzvQIMXd1702NtlOSPZKCYoP6zE8VU/vw1KsCYhot4ig/4xXm8oXHsnPnILOlBa1oqyfLTVDmaxgY+huPnKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T03:58:46.506490Z"},"content_sha256":"31da8815d3d47b218f32d6d5f419eb6eac562c25c9dea11a0c8227a41ca3fccf","schema_version":"1.0","event_id":"sha256:31da8815d3d47b218f32d6d5f419eb6eac562c25c9dea11a0c8227a41ca3fccf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:73VUO7QH2PTZQDKBKMCXN32KUO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Valter Moretti","submitted_at":"2021-07-10T20:18:02Z","abstract_excerpt":"We consider the global Hadamard condition and the notion of Hadamard parametrix whose use is pervasive in algebraic QFT in curved spacetime (see refences in the main text). We point out the existence of a technical problem in the literature concerning well-definedness of the global Hadamard parametrix in normal neighbourhoods of Cauchy surfaces. We discuss in particular the definition of the (signed) geodesic distance $\\sigma$ and related structures in an open neighbourhood of the diagonal of $M\\times M$ larger than $U\\times U$, for a normal convex neighborhood $U$, where $(M,g)$ is a Riemanni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04903","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/2107.04903/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":"2026-07-05T03:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7QSpW0+cIZXGNlweA6CEbrsY8QXFCgKaWrSA3ykQeygBYx01QLk4TNmRTLyHPWiDzDFJtSEW2D2Il59kW9sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T03:58:46.506992Z"},"content_sha256":"8eb3bbe07a2ba37a21f455ed421956e8432073f92c5846208479500643318714","schema_version":"1.0","event_id":"sha256:8eb3bbe07a2ba37a21f455ed421956e8432073f92c5846208479500643318714"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73VUO7QH2PTZQDKBKMCXN32KUO/bundle.json","state_url":"https://pith.science/pith/73VUO7QH2PTZQDKBKMCXN32KUO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73VUO7QH2PTZQDKBKMCXN32KUO/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":"2026-08-10T03:58:46Z","links":{"resolver":"https://pith.science/pith/73VUO7QH2PTZQDKBKMCXN32KUO","bundle":"https://pith.science/pith/73VUO7QH2PTZQDKBKMCXN32KUO/bundle.json","state":"https://pith.science/pith/73VUO7QH2PTZQDKBKMCXN32KUO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73VUO7QH2PTZQDKBKMCXN32KUO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:73VUO7QH2PTZQDKBKMCXN32KUO","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":"d4a5097660787414578ec679fdd61394f11bd799219598dda59864bc3d655682","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-07-10T20:18:02Z","title_canon_sha256":"fb8c9bd3c316d7fab9b01e471f8fe07af1949a34a8344f7664f14808ef452069"},"schema_version":"1.0","source":{"id":"2107.04903","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.04903","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2107.04903v2","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04903","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"73VUO7QH2PTZ","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"73VUO7QH2PTZQDKB","created_at":"2026-07-05T03:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"73VUO7QH","created_at":"2026-07-05T03:21:12Z"}],"graph_snapshots":[{"event_id":"sha256:8eb3bbe07a2ba37a21f455ed421956e8432073f92c5846208479500643318714","target":"graph","created_at":"2026-07-05T03:21:12Z","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/2107.04903/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the global Hadamard condition and the notion of Hadamard parametrix whose use is pervasive in algebraic QFT in curved spacetime (see refences in the main text). We point out the existence of a technical problem in the literature concerning well-definedness of the global Hadamard parametrix in normal neighbourhoods of Cauchy surfaces. We discuss in particular the definition of the (signed) geodesic distance $\\sigma$ and related structures in an open neighbourhood of the diagonal of $M\\times M$ larger than $U\\times U$, for a normal convex neighborhood $U$, where $(M,g)$ is a Riemanni","authors_text":"Valter Moretti","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-07-10T20:18:02Z","title":"On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04903","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":"sha256:31da8815d3d47b218f32d6d5f419eb6eac562c25c9dea11a0c8227a41ca3fccf","target":"record","created_at":"2026-07-05T03:21:12Z","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":"d4a5097660787414578ec679fdd61394f11bd799219598dda59864bc3d655682","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-07-10T20:18:02Z","title_canon_sha256":"fb8c9bd3c316d7fab9b01e471f8fe07af1949a34a8344f7664f14808ef452069"},"schema_version":"1.0","source":{"id":"2107.04903","kind":"arxiv","version":2}},"canonical_sha256":"feeb477e07d3e7980d41530576ef4aa39061c50e93f9987978a14c5ff7d2e4bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feeb477e07d3e7980d41530576ef4aa39061c50e93f9987978a14c5ff7d2e4bf","first_computed_at":"2026-07-05T03:21:12.456763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:21:12.456763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7F/OJ1hDfQCijFj1J+1QvKvA+sjfP922wvCCQEg20N/D3EHHdBsImRy8++4Q64y5qo62MdLstAhpfV92EeI3Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:21:12.457238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.04903","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31da8815d3d47b218f32d6d5f419eb6eac562c25c9dea11a0c8227a41ca3fccf","sha256:8eb3bbe07a2ba37a21f455ed421956e8432073f92c5846208479500643318714"],"state_sha256":"e44197cc25096204363aa7b10e44a645b9368a05497cfcaf44752fbbbfa30a51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZfSKzdnjB8dbvm3cpdoQYYjoPA47z6DCrp4vse31nU3nObGZ9r73DPUuKcH5hdyLCelRdbC9pQt7zmN+HNNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T03:58:46.510867Z","bundle_sha256":"deb7036aab187c2ca57b58c1b051383ad81e163a07cff2f4ddef31676206ecc5"}}