{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:D53M3HDOCWDZT53UYPDY44BIIP","short_pith_number":"pith:D53M3HDO","schema_version":"1.0","canonical_sha256":"1f76cd9c6e158799f774c3c78e702843d8c4bd9a5ccfdc31b81c9f0ff5920ac2","source":{"kind":"arxiv","id":"2101.09017","version":2},"attestation_state":"computed","paper":{"title":"Crossing Symmetric Dispersion Relations for Mellin Amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ahmadullah Zahed, Aninda Sinha, Rajesh Gopakumar","submitted_at":"2021-01-22T09:31:18Z","abstract_excerpt":"We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs). This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain \"locality\" constraints replacing the requirement of crossing symmetry in the usual fixed-$t$ dispersion relation. Using these constraints we show that the sum rules based on the two channel dispersion relations and the pres"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2101.09017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-01-22T09:31:18Z","cross_cats_sorted":[],"title_canon_sha256":"f1882a5a7020be504c272683d985ef6752e4220ab6974865630ab0b0cc934cac","abstract_canon_sha256":"0f2199bdf8c72530a6c13fdfe99d2499b77c398838a60c02da72e53e0d757a14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:44:05.119369Z","signature_b64":"syjRBMKb2SkR6NhUmwEifO5aAzQoQXk9HlngVvLTXAxxR87F928nCmK3/atxthC3JdTgKiqzjI4eaSj+dVy/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f76cd9c6e158799f774c3c78e702843d8c4bd9a5ccfdc31b81c9f0ff5920ac2","last_reissued_at":"2026-07-05T02:44:05.118896Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:44:05.118896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crossing Symmetric Dispersion Relations for Mellin Amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ahmadullah Zahed, Aninda Sinha, Rajesh Gopakumar","submitted_at":"2021-01-22T09:31:18Z","abstract_excerpt":"We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs). This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain \"locality\" constraints replacing the requirement of crossing symmetry in the usual fixed-$t$ dispersion relation. Using these constraints we show that the sum rules based on the two channel dispersion relations and the pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.09017","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/2101.09017/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2101.09017","created_at":"2026-07-05T02:44:05.118955+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.09017v2","created_at":"2026-07-05T02:44:05.118955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.09017","created_at":"2026-07-05T02:44:05.118955+00:00"},{"alias_kind":"pith_short_12","alias_value":"D53M3HDOCWDZ","created_at":"2026-07-05T02:44:05.118955+00:00"},{"alias_kind":"pith_short_16","alias_value":"D53M3HDOCWDZT53U","created_at":"2026-07-05T02:44:05.118955+00:00"},{"alias_kind":"pith_short_8","alias_value":"D53M3HDO","created_at":"2026-07-05T02:44:05.118955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.18929","citing_title":"Higher-Trace Operators and Cut Diagrammatics in the Conformal Block Expansion","ref_index":55,"is_internal_anchor":false},{"citing_arxiv_id":"2606.17719","citing_title":"Aspects of Witten Diagrams for Holographic Defects","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP","json":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP.json","graph_json":"https://pith.science/api/pith-number/D53M3HDOCWDZT53UYPDY44BIIP/graph.json","events_json":"https://pith.science/api/pith-number/D53M3HDOCWDZT53UYPDY44BIIP/events.json","paper":"https://pith.science/paper/D53M3HDO"},"agent_actions":{"view_html":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP","download_json":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP.json","view_paper":"https://pith.science/paper/D53M3HDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.09017&json=true","fetch_graph":"https://pith.science/api/pith-number/D53M3HDOCWDZT53UYPDY44BIIP/graph.json","fetch_events":"https://pith.science/api/pith-number/D53M3HDOCWDZT53UYPDY44BIIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP/action/storage_attestation","attest_author":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP/action/author_attestation","sign_citation":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP/action/citation_signature","submit_replication":"https://pith.science/pith/D53M3HDOCWDZT53UYPDY44BIIP/action/replication_record"}},"created_at":"2026-07-05T02:44:05.118955+00:00","updated_at":"2026-07-05T02:44:05.118955+00:00"}