{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:7DJNWRL2HEYWRC7EOWIQCQEBFA","short_pith_number":"pith:7DJNWRL2","schema_version":"1.0","canonical_sha256":"f8d2db457a3931688be4759101408128223ecef71b15b6e67a7b8331e3e1f5d1","source":{"kind":"arxiv","id":"2108.10355","version":2},"attestation_state":"computed","paper":{"title":"Positivity and Geometric Function Theory Constraints on Pion Scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Ahmadullah Zahed","submitted_at":"2021-08-23T18:29:42Z","abstract_excerpt":"This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with $O(N)$ global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the $z$-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for $O(N)$ model in $z$-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the $O(N)$ model arising from the fully crossing s"},"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":"2108.10355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-23T18:29:42Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"0b07124204865036d136f0bc36c15d03edb13ce7d3d9257f9682c80680d7245d","abstract_canon_sha256":"863f2d506e71c0e37065953bf79b6e9105b09e1b8146595bd16162db9822ffe7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:39:34.873306Z","signature_b64":"Prq7cDWVtzrgHx/B13VGItFmZ0K7aQP+r2OtfoWMAvPXXQFWwDQNMec6OWd67lR4KY5iExRu5ZT1+DFVDgI6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8d2db457a3931688be4759101408128223ecef71b15b6e67a7b8331e3e1f5d1","last_reissued_at":"2026-07-05T03:39:34.872782Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:39:34.872782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positivity and Geometric Function Theory Constraints on Pion Scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Ahmadullah Zahed","submitted_at":"2021-08-23T18:29:42Z","abstract_excerpt":"This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with $O(N)$ global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the $z$-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for $O(N)$ model in $z$-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the $O(N)$ model arising from the fully crossing s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.10355","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/2108.10355/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":"2108.10355","created_at":"2026-07-05T03:39:34.872856+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.10355v2","created_at":"2026-07-05T03:39:34.872856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.10355","created_at":"2026-07-05T03:39:34.872856+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DJNWRL2HEYW","created_at":"2026-07-05T03:39:34.872856+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DJNWRL2HEYWRC7E","created_at":"2026-07-05T03:39:34.872856+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DJNWRL2","created_at":"2026-07-05T03:39:34.872856+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA","json":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA.json","graph_json":"https://pith.science/api/pith-number/7DJNWRL2HEYWRC7EOWIQCQEBFA/graph.json","events_json":"https://pith.science/api/pith-number/7DJNWRL2HEYWRC7EOWIQCQEBFA/events.json","paper":"https://pith.science/paper/7DJNWRL2"},"agent_actions":{"view_html":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA","download_json":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA.json","view_paper":"https://pith.science/paper/7DJNWRL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.10355&json=true","fetch_graph":"https://pith.science/api/pith-number/7DJNWRL2HEYWRC7EOWIQCQEBFA/graph.json","fetch_events":"https://pith.science/api/pith-number/7DJNWRL2HEYWRC7EOWIQCQEBFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA/action/storage_attestation","attest_author":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA/action/author_attestation","sign_citation":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA/action/citation_signature","submit_replication":"https://pith.science/pith/7DJNWRL2HEYWRC7EOWIQCQEBFA/action/replication_record"}},"created_at":"2026-07-05T03:39:34.872856+00:00","updated_at":"2026-07-05T03:39:34.872856+00:00"}