{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:CIK7C4WEGILVMUMO6ZIAVN6CUL","short_pith_number":"pith:CIK7C4WE","canonical_record":{"source":{"id":"2203.04269","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-03-08T18:42:53Z","cross_cats_sorted":[],"title_canon_sha256":"1e00733125713cc0bde0e2f80ed616c565643d6c3c75d15bdf902bceb5f158f4","abstract_canon_sha256":"5cca969ae64e3e576632bcc8e99ecbc1a393e621015534432b4b50c8fae9af1e"},"schema_version":"1.0"},"canonical_sha256":"1215f172c4321756518ef6500ab7c2a2fc8467df197c8e63ef0ac996ec5d8850","source":{"kind":"arxiv","id":"2203.04269","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.04269","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"2203.04269v2","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.04269","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"CIK7C4WEGILV","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"CIK7C4WEGILVMUMO","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"CIK7C4WE","created_at":"2026-07-05T05:33:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:CIK7C4WEGILVMUMO6ZIAVN6CUL","target":"record","payload":{"canonical_record":{"source":{"id":"2203.04269","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-03-08T18:42:53Z","cross_cats_sorted":[],"title_canon_sha256":"1e00733125713cc0bde0e2f80ed616c565643d6c3c75d15bdf902bceb5f158f4","abstract_canon_sha256":"5cca969ae64e3e576632bcc8e99ecbc1a393e621015534432b4b50c8fae9af1e"},"schema_version":"1.0"},"canonical_sha256":"1215f172c4321756518ef6500ab7c2a2fc8467df197c8e63ef0ac996ec5d8850","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:33:08.983018Z","signature_b64":"vPFBp9Tfsl7KSqlr3du99nyhd8SvRTmGu162fiQDncxBY5Iu5dyDMJpqmgBK5o7iVIww7LQC0gdPYVaLaJ4DCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1215f172c4321756518ef6500ab7c2a2fc8467df197c8e63ef0ac996ec5d8850","last_reissued_at":"2026-07-05T05:33:08.982425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:33:08.982425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.04269","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":"2026-07-05T05:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z4wFtXRyFvjTZb5r8e21U9JAuwviuGj14dq9jqzrC3NBHAJ2y08OAizhz0aAjV83RdPPM9evMrOM0BNk3L11BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:47:47.082967Z"},"content_sha256":"f8a242799f1e876d8cb33622cb367a24922eb6e5005574d3354a1027df8ae42f","schema_version":"1.0","event_id":"sha256:f8a242799f1e876d8cb33622cb367a24922eb6e5005574d3354a1027df8ae42f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:CIK7C4WEGILVMUMO6ZIAVN6CUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ans\\\"atze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ben Page, Giuseppe De Laurentis","submitted_at":"2022-03-08T18:42:53Z","abstract_excerpt":"Rational coefficients of special functions in scattering amplitudes are known to simplify on singular surfaces, often diverging less strongly than the na\\\"ive expectation. To systematically study these surfaces and rational functions on them, we employ tools from algebraic geometry. We show how the divergences of a rational function constrain its numerator to belong to symbolic powers of ideals associated to the singular surfaces. To study the divergences of the coefficients, we make use of $p$-adic numbers, closely related to finite fields. These allow us to perform numerical evaluations clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04269","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/2203.04269/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":"2026-07-05T05:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NLirlI9iOUsZZl2Wc+4uAXQY7XUYEaTBd0dQVSR5BkKZne7uz++AjCpxHiDzKQX3jO3cKlffRBaQ+0+BsdZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:47:47.083483Z"},"content_sha256":"b7349c69c14b3d8d3be23a5035e233900fcc832a9cff94d319256f31ec32712c","schema_version":"1.0","event_id":"sha256:b7349c69c14b3d8d3be23a5035e233900fcc832a9cff94d319256f31ec32712c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/bundle.json","state_url":"https://pith.science/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/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":"2026-08-06T08:47:47Z","links":{"resolver":"https://pith.science/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL","bundle":"https://pith.science/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/bundle.json","state":"https://pith.science/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIK7C4WEGILVMUMO6ZIAVN6CUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CIK7C4WEGILVMUMO6ZIAVN6CUL","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":"5cca969ae64e3e576632bcc8e99ecbc1a393e621015534432b4b50c8fae9af1e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-03-08T18:42:53Z","title_canon_sha256":"1e00733125713cc0bde0e2f80ed616c565643d6c3c75d15bdf902bceb5f158f4"},"schema_version":"1.0","source":{"id":"2203.04269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.04269","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"2203.04269v2","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.04269","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"CIK7C4WEGILV","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"CIK7C4WEGILVMUMO","created_at":"2026-07-05T05:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"CIK7C4WE","created_at":"2026-07-05T05:33:08Z"}],"graph_snapshots":[{"event_id":"sha256:b7349c69c14b3d8d3be23a5035e233900fcc832a9cff94d319256f31ec32712c","target":"graph","created_at":"2026-07-05T05:33:08Z","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/2203.04269/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Rational coefficients of special functions in scattering amplitudes are known to simplify on singular surfaces, often diverging less strongly than the na\\\"ive expectation. To systematically study these surfaces and rational functions on them, we employ tools from algebraic geometry. We show how the divergences of a rational function constrain its numerator to belong to symbolic powers of ideals associated to the singular surfaces. To study the divergences of the coefficients, we make use of $p$-adic numbers, closely related to finite fields. These allow us to perform numerical evaluations clos","authors_text":"Ben Page, Giuseppe De Laurentis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-03-08T18:42:53Z","title":"Ans\\\"atze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04269","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:f8a242799f1e876d8cb33622cb367a24922eb6e5005574d3354a1027df8ae42f","target":"record","created_at":"2026-07-05T05:33:08Z","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":"5cca969ae64e3e576632bcc8e99ecbc1a393e621015534432b4b50c8fae9af1e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-03-08T18:42:53Z","title_canon_sha256":"1e00733125713cc0bde0e2f80ed616c565643d6c3c75d15bdf902bceb5f158f4"},"schema_version":"1.0","source":{"id":"2203.04269","kind":"arxiv","version":2}},"canonical_sha256":"1215f172c4321756518ef6500ab7c2a2fc8467df197c8e63ef0ac996ec5d8850","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1215f172c4321756518ef6500ab7c2a2fc8467df197c8e63ef0ac996ec5d8850","first_computed_at":"2026-07-05T05:33:08.982425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:33:08.982425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPFBp9Tfsl7KSqlr3du99nyhd8SvRTmGu162fiQDncxBY5Iu5dyDMJpqmgBK5o7iVIww7LQC0gdPYVaLaJ4DCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:33:08.983018Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.04269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a242799f1e876d8cb33622cb367a24922eb6e5005574d3354a1027df8ae42f","sha256:b7349c69c14b3d8d3be23a5035e233900fcc832a9cff94d319256f31ec32712c"],"state_sha256":"90533e8046a10e4970b1c854bd1304d39c71e59a051bd1077a133631f7da5e9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pg8lnXoL7/xypHWAJ3f+GwCgPxQXYRAunoVhqI6JibWpmCdjY1dU60CBO3TL2ADlO3BNSFryCp82qvru6szDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:47:47.088582Z","bundle_sha256":"2a59df4c23e83f576fd0201a22a4afce9ab15024f358316c77c2401269ac5979"}}