{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:6V5NBPYPQGYGZEVBNMH2JWP2FQ","short_pith_number":"pith:6V5NBPYP","canonical_record":{"source":{"id":"hep-ph/9809568","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-28T17:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"9fb1d95e68ea658d5c4590713fab583ff79d32cd932fdfc7e8a272d505da1f96","abstract_canon_sha256":"3519ea1456effca5d19e8e55d829d71453f57f25e3e0f4e0e28b23f4d1d5a4b3"},"schema_version":"1.0"},"canonical_sha256":"f57ad0bf0f81b06c92a16b0fa4d9fa2c2909390c567cec7ade14855fe6187f22","source":{"kind":"arxiv","id":"hep-ph/9809568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9809568","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9809568v1","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9809568","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"6V5NBPYPQGYG","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"6V5NBPYPQGYGZEVB","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"6V5NBPYP","created_at":"2026-07-04T16:09:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:6V5NBPYPQGYGZEVBNMH2JWP2FQ","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/9809568","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-28T17:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"9fb1d95e68ea658d5c4590713fab583ff79d32cd932fdfc7e8a272d505da1f96","abstract_canon_sha256":"3519ea1456effca5d19e8e55d829d71453f57f25e3e0f4e0e28b23f4d1d5a4b3"},"schema_version":"1.0"},"canonical_sha256":"f57ad0bf0f81b06c92a16b0fa4d9fa2c2909390c567cec7ade14855fe6187f22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:09:31.975668Z","signature_b64":"2+e6/z8RDlgZyfzZqREZcBizN8lvUryCtWKbTWwJ44On31ei7EIABPzbVxN+uUufSS4Bdla2dXT8kopbnx0pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f57ad0bf0f81b06c92a16b0fa4d9fa2c2909390c567cec7ade14855fe6187f22","last_reissued_at":"2026-07-04T16:09:31.975278Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:09:31.975278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/9809568","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iuF+LgyeXsX4YhyqynDVRym1mhTxtWqTRGuiyw3PE7EjyE8KyhwsaLCfgrlql5SiaV/Bq97mCWPdjdaYe+T+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:12:58.995603Z"},"content_sha256":"3eb7bcd9027dca51e075d8253aab18e0b42757e2dde7534169be1e128e4162be","schema_version":"1.0","event_id":"sha256:3eb7bcd9027dca51e075d8253aab18e0b42757e2dde7534169be1e128e4162be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:6V5NBPYPQGYGZEVBNMH2JWP2FQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Petre Di\\c{t}\\u{a} (NIPNE - Bucharest)","submitted_at":"1998-09-28T17:03:20Z","abstract_excerpt":"We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination $b_3+3 b_4$ are positive quantities. The two-loops approximation gives inequalities involving all the six arbitrary parameters entering ChPT amplitude, but the corrections to the one-loop approximation results are small. ChPT amplitudes pass unexpectedly well all the positivity tests giving s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9809568","kind":"arxiv","version":1},"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/hep-ph/9809568/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":"2026-07-04T16:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDTjPd4/tqHCXG3+/0tYl0MBRxofJ/0kSrMWDVgD2lkrjjPrBPSRqb8VwXJGGcMwDk5kb8gfC4odEehjqVdoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:12:58.996111Z"},"content_sha256":"95801e41fda8b44a5e687bf15c3705f2eec95c812c62cebd4b19d550b0e6995a","schema_version":"1.0","event_id":"sha256:95801e41fda8b44a5e687bf15c3705f2eec95c812c62cebd4b19d550b0e6995a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/bundle.json","state_url":"https://pith.science/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/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":"2026-08-16T19:12:58Z","links":{"resolver":"https://pith.science/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ","bundle":"https://pith.science/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/bundle.json","state":"https://pith.science/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6V5NBPYPQGYGZEVBNMH2JWP2FQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:6V5NBPYPQGYGZEVBNMH2JWP2FQ","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":"3519ea1456effca5d19e8e55d829d71453f57f25e3e0f4e0e28b23f4d1d5a4b3","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-28T17:03:20Z","title_canon_sha256":"9fb1d95e68ea658d5c4590713fab583ff79d32cd932fdfc7e8a272d505da1f96"},"schema_version":"1.0","source":{"id":"hep-ph/9809568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9809568","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9809568v1","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9809568","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"6V5NBPYPQGYG","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"6V5NBPYPQGYGZEVB","created_at":"2026-07-04T16:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"6V5NBPYP","created_at":"2026-07-04T16:09:31Z"}],"graph_snapshots":[{"event_id":"sha256:95801e41fda8b44a5e687bf15c3705f2eec95c812c62cebd4b19d550b0e6995a","target":"graph","created_at":"2026-07-04T16:09:31Z","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/hep-ph/9809568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination $b_3+3 b_4$ are positive quantities. The two-loops approximation gives inequalities involving all the six arbitrary parameters entering ChPT amplitude, but the corrections to the one-loop approximation results are small. ChPT amplitudes pass unexpectedly well all the positivity tests giving s","authors_text":"Petre Di\\c{t}\\u{a} (NIPNE - Bucharest)","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1998-09-28T17:03:20Z","title":"Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9809568","kind":"arxiv","version":1},"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":"sha256:3eb7bcd9027dca51e075d8253aab18e0b42757e2dde7534169be1e128e4162be","target":"record","created_at":"2026-07-04T16:09:31Z","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":"3519ea1456effca5d19e8e55d829d71453f57f25e3e0f4e0e28b23f4d1d5a4b3","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-28T17:03:20Z","title_canon_sha256":"9fb1d95e68ea658d5c4590713fab583ff79d32cd932fdfc7e8a272d505da1f96"},"schema_version":"1.0","source":{"id":"hep-ph/9809568","kind":"arxiv","version":1}},"canonical_sha256":"f57ad0bf0f81b06c92a16b0fa4d9fa2c2909390c567cec7ade14855fe6187f22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f57ad0bf0f81b06c92a16b0fa4d9fa2c2909390c567cec7ade14855fe6187f22","first_computed_at":"2026-07-04T16:09:31.975278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:09:31.975278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2+e6/z8RDlgZyfzZqREZcBizN8lvUryCtWKbTWwJ44On31ei7EIABPzbVxN+uUufSS4Bdla2dXT8kopbnx0pAA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:09:31.975668Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9809568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eb7bcd9027dca51e075d8253aab18e0b42757e2dde7534169be1e128e4162be","sha256:95801e41fda8b44a5e687bf15c3705f2eec95c812c62cebd4b19d550b0e6995a"],"state_sha256":"b46bfa106f6b747d9ffee6c49cec1e76c1a45a57dddefb7b9280de47dbefbea3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eL5B/HNQfJxgNSYUJvW+hn0pkuoNNpQI8cI/mdeTLkbr4SXZY87mBh/4IoTMYbe7LS+eyy4RYnwze01v88rJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:12:59.001342Z","bundle_sha256":"cc9626cb3ca28c8968f92c04904b10875f9401cd2f5b2cb5ac7dfda9f93b08bf"}}