{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:G2MT5TEP4E5IPGF2KQWW63XG7M","short_pith_number":"pith:G2MT5TEP","canonical_record":{"source":{"id":"2207.12464","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-07-25T18:29:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"06c1c14448b23a7e5577fe9afb33121171ef96deb006306f66dbbd40e07d81c0","abstract_canon_sha256":"d59af760904e29376041eabee31dda96e493d61ad1c35e1af39406c281f5b0d6"},"schema_version":"1.0"},"canonical_sha256":"36993ecc8fe13a8798ba542d6f6ee6fb27dbdeb401f6966716e2b9fad44ef68d","source":{"kind":"arxiv","id":"2207.12464","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.12464","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"2207.12464v2","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12464","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"G2MT5TEP4E5I","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_16","alias_value":"G2MT5TEP4E5IPGF2","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_8","alias_value":"G2MT5TEP","created_at":"2026-07-05T06:49:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:G2MT5TEP4E5IPGF2KQWW63XG7M","target":"record","payload":{"canonical_record":{"source":{"id":"2207.12464","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-07-25T18:29:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"06c1c14448b23a7e5577fe9afb33121171ef96deb006306f66dbbd40e07d81c0","abstract_canon_sha256":"d59af760904e29376041eabee31dda96e493d61ad1c35e1af39406c281f5b0d6"},"schema_version":"1.0"},"canonical_sha256":"36993ecc8fe13a8798ba542d6f6ee6fb27dbdeb401f6966716e2b9fad44ef68d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:49:57.744768Z","signature_b64":"RmYi93+/6/8wQy0bQw6vt2M2Yu7euoCq7B371dkMQ5mipb7VLWN5z6/1SJDwyePDBaZeObVJeBNAGzM3uUaGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36993ecc8fe13a8798ba542d6f6ee6fb27dbdeb401f6966716e2b9fad44ef68d","last_reissued_at":"2026-07-05T06:49:57.744328Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:49:57.744328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.12464","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":"2026-07-05T06:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BqichwN4Bv9Nj2iH1/0T+p5M3YGcOqC2criXa0QgiuieWsjb2PwepWmijexlNUxBBWAI1nQPjZKwAIJVQqbpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T15:41:59.216864Z"},"content_sha256":"205a8e129f3d3c370cff19e814d6b531192c5f1dfd7ffc5ed245f86dd5fc911c","schema_version":"1.0","event_id":"sha256:205a8e129f3d3c370cff19e814d6b531192c5f1dfd7ffc5ed245f86dd5fc911c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:G2MT5TEP4E5IPGF2KQWW63XG7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Internal boundaries of the loop amplituhedron","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Alastair Stewart, Gabriele Dian, Paul Heslop","submitted_at":"2022-07-25T18:29:39Z","abstract_excerpt":"The strict definition of positive geometry implies that all maximal residues of its canonical form are $\\pm 1$. We observe, however, that the loop integrand of the amplitude in planar $\\mathcal{N}=4$ super Yang-Mills has maximal residues not equal to $\\pm 1$. We find the reason for this is that deep in the boundary structure of the loop amplituhedron there are geometries which contain internal boundaries: codimension one defects separating two regions of opposite orientation. This phenomenon requires a generalisation of the concept of positive geometry and canonical form to include such intern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12464","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/2207.12464/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":"2026-07-05T06:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pymUfhwi0CH9g2qwSOAtcQjMO2Zcuk5+oWKxrM9Q8fJeWNo76g/azev9z+400KRj2b4T2S1tbAlzKlNcxVNYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T15:41:59.217377Z"},"content_sha256":"339a55d2004a2dcb82be51addbd70d4d0f4dd01c0ccdd64937ad2870479915e8","schema_version":"1.0","event_id":"sha256:339a55d2004a2dcb82be51addbd70d4d0f4dd01c0ccdd64937ad2870479915e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/bundle.json","state_url":"https://pith.science/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/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":"2026-08-07T15:41:59Z","links":{"resolver":"https://pith.science/pith/G2MT5TEP4E5IPGF2KQWW63XG7M","bundle":"https://pith.science/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/bundle.json","state":"https://pith.science/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2MT5TEP4E5IPGF2KQWW63XG7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:G2MT5TEP4E5IPGF2KQWW63XG7M","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":"d59af760904e29376041eabee31dda96e493d61ad1c35e1af39406c281f5b0d6","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-07-25T18:29:39Z","title_canon_sha256":"06c1c14448b23a7e5577fe9afb33121171ef96deb006306f66dbbd40e07d81c0"},"schema_version":"1.0","source":{"id":"2207.12464","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.12464","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"2207.12464v2","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12464","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"G2MT5TEP4E5I","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_16","alias_value":"G2MT5TEP4E5IPGF2","created_at":"2026-07-05T06:49:57Z"},{"alias_kind":"pith_short_8","alias_value":"G2MT5TEP","created_at":"2026-07-05T06:49:57Z"}],"graph_snapshots":[{"event_id":"sha256:339a55d2004a2dcb82be51addbd70d4d0f4dd01c0ccdd64937ad2870479915e8","target":"graph","created_at":"2026-07-05T06:49:57Z","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/2207.12464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The strict definition of positive geometry implies that all maximal residues of its canonical form are $\\pm 1$. We observe, however, that the loop integrand of the amplitude in planar $\\mathcal{N}=4$ super Yang-Mills has maximal residues not equal to $\\pm 1$. We find the reason for this is that deep in the boundary structure of the loop amplituhedron there are geometries which contain internal boundaries: codimension one defects separating two regions of opposite orientation. This phenomenon requires a generalisation of the concept of positive geometry and canonical form to include such intern","authors_text":"Alastair Stewart, Gabriele Dian, Paul Heslop","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-07-25T18:29:39Z","title":"Internal boundaries of the loop amplituhedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12464","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":"sha256:205a8e129f3d3c370cff19e814d6b531192c5f1dfd7ffc5ed245f86dd5fc911c","target":"record","created_at":"2026-07-05T06:49:57Z","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":"d59af760904e29376041eabee31dda96e493d61ad1c35e1af39406c281f5b0d6","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-07-25T18:29:39Z","title_canon_sha256":"06c1c14448b23a7e5577fe9afb33121171ef96deb006306f66dbbd40e07d81c0"},"schema_version":"1.0","source":{"id":"2207.12464","kind":"arxiv","version":2}},"canonical_sha256":"36993ecc8fe13a8798ba542d6f6ee6fb27dbdeb401f6966716e2b9fad44ef68d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36993ecc8fe13a8798ba542d6f6ee6fb27dbdeb401f6966716e2b9fad44ef68d","first_computed_at":"2026-07-05T06:49:57.744328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:49:57.744328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RmYi93+/6/8wQy0bQw6vt2M2Yu7euoCq7B371dkMQ5mipb7VLWN5z6/1SJDwyePDBaZeObVJeBNAGzM3uUaGDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:49:57.744768Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.12464","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:205a8e129f3d3c370cff19e814d6b531192c5f1dfd7ffc5ed245f86dd5fc911c","sha256:339a55d2004a2dcb82be51addbd70d4d0f4dd01c0ccdd64937ad2870479915e8"],"state_sha256":"2f3e1a8225846b6a6c7eb1770b1c81923a6964020f2cff2e932f5dbe9354048f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLSGGT639BAe5XnAefF0AO8BLd4twjI1El7+9QJt1PBfTL+52RSmQlrC92c2LfZ6GeiYDkMaoRdHdsaYhVFOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T15:41:59.221224Z","bundle_sha256":"c4c8fd4533251a2ef4ad2a737987f0aee2094f2d283e5567516b98e89daaaf16"}}