{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KMUBOZWGAYW4E3FX2VVVPWZYYP","short_pith_number":"pith:KMUBOZWG","canonical_record":{"source":{"id":"1303.4377","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T19:45:23Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"1512625434a9574bed1cfe0d5cbe82eb8a632aa7c91bc53bdd17d0d1692094ff","abstract_canon_sha256":"e86af6e5f459d7d9f39ec29be4086c6adeae937db2c22af2c99e36e501bdd6f1"},"schema_version":"1.0"},"canonical_sha256":"53281766c6062dc26cb7d56b57db38c3c9b2424c45b69e53c393d331cc912ba2","source":{"kind":"arxiv","id":"1303.4377","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4377","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4377v3","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4377","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"KMUBOZWGAYW4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KMUBOZWGAYW4E3FX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KMUBOZWG","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KMUBOZWGAYW4E3FX2VVVPWZYYP","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4377","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T19:45:23Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"1512625434a9574bed1cfe0d5cbe82eb8a632aa7c91bc53bdd17d0d1692094ff","abstract_canon_sha256":"e86af6e5f459d7d9f39ec29be4086c6adeae937db2c22af2c99e36e501bdd6f1"},"schema_version":"1.0"},"canonical_sha256":"53281766c6062dc26cb7d56b57db38c3c9b2424c45b69e53c393d331cc912ba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:18.367938Z","signature_b64":"dMFivu+8FYQrdGqeguzfMgS99aZzXxJ40Jku947EeYCTF3uzydZC2Pibh1o90pBVxTbvJ8W8jEE/+Odq/1YQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53281766c6062dc26cb7d56b57db38c3c9b2424c45b69e53c393d331cc912ba2","last_reissued_at":"2026-05-18T02:49:18.367218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:18.367218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4377","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z05Pd+HvXM6Ckvu/9p18TKtsWFJGYj97OSEGyhV85hD6r6pl5NOQ1i8lBe/R/VlfQ9uGc/seTM7FhaRlSLE8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:43:48.045908Z"},"content_sha256":"8412035d377ef6530895bfda52bbc4e95813497efa86734b49a6b7020e077ddb","schema_version":"1.0","event_id":"sha256:8412035d377ef6530895bfda52bbc4e95813497efa86734b49a6b7020e077ddb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KMUBOZWGAYW4E3FX2VVVPWZYYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hertz potentials and asymptotic properties of massless fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"J\\'er\\'emie Joudioux, Lars Andersson, Thomas B\\\"ackdahl","submitted_at":"2013-03-18T19:45:23Z","abstract_excerpt":"In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4377","kind":"arxiv","version":3},"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":"2026-05-18T02:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6icHnG4bShZoBNMGta1ZLcAN+EmD1eHco+7Js+rA0YvaRvMVnjOCRXYtN9ufP1///n7ma51Qh00ssV8hAzTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:43:48.046534Z"},"content_sha256":"79e92533c42279bca6ee5c57f460e38f4e828ac92e118f0dc24f39cbd88e05d8","schema_version":"1.0","event_id":"sha256:79e92533c42279bca6ee5c57f460e38f4e828ac92e118f0dc24f39cbd88e05d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/bundle.json","state_url":"https://pith.science/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/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":"2026-05-28T08:43:48Z","links":{"resolver":"https://pith.science/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP","bundle":"https://pith.science/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/bundle.json","state":"https://pith.science/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMUBOZWGAYW4E3FX2VVVPWZYYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KMUBOZWGAYW4E3FX2VVVPWZYYP","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":"e86af6e5f459d7d9f39ec29be4086c6adeae937db2c22af2c99e36e501bdd6f1","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T19:45:23Z","title_canon_sha256":"1512625434a9574bed1cfe0d5cbe82eb8a632aa7c91bc53bdd17d0d1692094ff"},"schema_version":"1.0","source":{"id":"1303.4377","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4377","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4377v3","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4377","created_at":"2026-05-18T02:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"KMUBOZWGAYW4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KMUBOZWGAYW4E3FX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KMUBOZWG","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:79e92533c42279bca6ee5c57f460e38f4e828ac92e118f0dc24f39cbd88e05d8","target":"graph","created_at":"2026-05-18T02:49:18Z","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":"In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.","authors_text":"J\\'er\\'emie Joudioux, Lars Andersson, Thomas B\\\"ackdahl","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T19:45:23Z","title":"Hertz potentials and asymptotic properties of massless fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4377","kind":"arxiv","version":3},"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":"sha256:8412035d377ef6530895bfda52bbc4e95813497efa86734b49a6b7020e077ddb","target":"record","created_at":"2026-05-18T02:49:18Z","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":"e86af6e5f459d7d9f39ec29be4086c6adeae937db2c22af2c99e36e501bdd6f1","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T19:45:23Z","title_canon_sha256":"1512625434a9574bed1cfe0d5cbe82eb8a632aa7c91bc53bdd17d0d1692094ff"},"schema_version":"1.0","source":{"id":"1303.4377","kind":"arxiv","version":3}},"canonical_sha256":"53281766c6062dc26cb7d56b57db38c3c9b2424c45b69e53c393d331cc912ba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53281766c6062dc26cb7d56b57db38c3c9b2424c45b69e53c393d331cc912ba2","first_computed_at":"2026-05-18T02:49:18.367218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:18.367218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dMFivu+8FYQrdGqeguzfMgS99aZzXxJ40Jku947EeYCTF3uzydZC2Pibh1o90pBVxTbvJ8W8jEE/+Odq/1YQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:18.367938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4377","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8412035d377ef6530895bfda52bbc4e95813497efa86734b49a6b7020e077ddb","sha256:79e92533c42279bca6ee5c57f460e38f4e828ac92e118f0dc24f39cbd88e05d8"],"state_sha256":"ec23a4e743b286398406868b86367865e9138186f845b6c8204f2fe87c03c38e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4BByR70wQ7rsgOthIKv4XpLLM/shBndzwOlENp6bHoPAHgUu+wUqe81o/nQq9HJ7zuE5iWgeiEoNc2gkilZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:43:48.049405Z","bundle_sha256":"e15c11314b306a96a5f3f6ac45f94918353012d224677ef2a6a3f058c3ebc9b1"}}