{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FQMZYECSGG6BGP4BOH5ZGBKLR4","short_pith_number":"pith:FQMZYECS","canonical_record":{"source":{"id":"2603.03183","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-03-03T17:42:42Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"d8b16420e7b46cffb37d23864879f1fe8c92aff9d3b753b28f77896bb40a8094","abstract_canon_sha256":"d77a537488750603642b62b7e3a30490615c21b4b21487eec1b0ec52374e5d5f"},"schema_version":"1.0"},"canonical_sha256":"2c199c105231bc133f8171fb93054b8f069e2cedf4bcf5323f76d56785ac632e","source":{"kind":"arxiv","id":"2603.03183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03183","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03183v2","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03183","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"FQMZYECSGG6B","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_16","alias_value":"FQMZYECSGG6BGP4B","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_8","alias_value":"FQMZYECS","created_at":"2026-07-16T01:22:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FQMZYECSGG6BGP4BOH5ZGBKLR4","target":"record","payload":{"canonical_record":{"source":{"id":"2603.03183","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-03-03T17:42:42Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"d8b16420e7b46cffb37d23864879f1fe8c92aff9d3b753b28f77896bb40a8094","abstract_canon_sha256":"d77a537488750603642b62b7e3a30490615c21b4b21487eec1b0ec52374e5d5f"},"schema_version":"1.0"},"canonical_sha256":"2c199c105231bc133f8171fb93054b8f069e2cedf4bcf5323f76d56785ac632e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:35.513978Z","signature_b64":"Yn1Uo3ywr8p6RDnbEjiWORjEcbmtOa+EVh/taCohqqFr9GjiKg2BjRo+eJRjkYBxbqpENYT5MK+xmJvFUiwFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c199c105231bc133f8171fb93054b8f069e2cedf4bcf5323f76d56785ac632e","last_reissued_at":"2026-07-16T01:22:35.513054Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:35.513054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.03183","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":"2026-07-16T01:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgq8Z0jBSbhymV4bQK53wmr4t4mrTlK8StuMES6Hv8q8B3kU+uI+n5B3nYYbbxyuOmpOZbxt3dcCrefCmMs2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:26:06.169884Z"},"content_sha256":"f29390a193fe4b01999706a0e89fa970525dde254e9b9b98ac81dcbcf7a5b832","schema_version":"1.0","event_id":"sha256:f29390a193fe4b01999706a0e89fa970525dde254e9b9b98ac81dcbcf7a5b832"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FQMZYECSGG6BGP4BOH5ZGBKLR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multiloop sunset to all orders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Pierre Vanhove","submitted_at":"2026-03-03T17:42:42Z","abstract_excerpt":"We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric polynomials in logarithmic mass ratios, normalized by the external momentum squared, with coefficients determined by analytic series expansions. For the equal-mass case, we establish a dimension-lowering relation expressing the $L$ loop sunset integrals in $D+2$ as the one in $D$ dimensions acted on a differential operator of order $L-1$.\n  These representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03183","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/2603.03183/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":"2026-07-16T01:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISTy+o9+xWT4cVNB+c2ZcSewOcT2PKnylH7JYPWmySNu+PE4w+VU1ZA8ZwpMOgQpw90uXD9H8Jn9Remve4JHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:26:06.170276Z"},"content_sha256":"f068f0cf9e8d2bb71f1ae45d00f014ee7a8596844724c20d6e502f6d0b4aca20","schema_version":"1.0","event_id":"sha256:f068f0cf9e8d2bb71f1ae45d00f014ee7a8596844724c20d6e502f6d0b4aca20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/bundle.json","state_url":"https://pith.science/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/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":"2026-08-04T00:26:06Z","links":{"resolver":"https://pith.science/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4","bundle":"https://pith.science/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/bundle.json","state":"https://pith.science/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQMZYECSGG6BGP4BOH5ZGBKLR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FQMZYECSGG6BGP4BOH5ZGBKLR4","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":"d77a537488750603642b62b7e3a30490615c21b4b21487eec1b0ec52374e5d5f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-03-03T17:42:42Z","title_canon_sha256":"d8b16420e7b46cffb37d23864879f1fe8c92aff9d3b753b28f77896bb40a8094"},"schema_version":"1.0","source":{"id":"2603.03183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03183","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03183v2","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03183","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"FQMZYECSGG6B","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_16","alias_value":"FQMZYECSGG6BGP4B","created_at":"2026-07-16T01:22:35Z"},{"alias_kind":"pith_short_8","alias_value":"FQMZYECS","created_at":"2026-07-16T01:22:35Z"}],"graph_snapshots":[{"event_id":"sha256:f068f0cf9e8d2bb71f1ae45d00f014ee7a8596844724c20d6e502f6d0b4aca20","target":"graph","created_at":"2026-07-16T01:22:35Z","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/2603.03183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric polynomials in logarithmic mass ratios, normalized by the external momentum squared, with coefficients determined by analytic series expansions. For the equal-mass case, we establish a dimension-lowering relation expressing the $L$ loop sunset integrals in $D+2$ as the one in $D$ dimensions acted on a differential operator of order $L-1$.\n  These representati","authors_text":"Pierre Vanhove","cross_cats":["hep-ph","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-03-03T17:42:42Z","title":"The multiloop sunset to all orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03183","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:f29390a193fe4b01999706a0e89fa970525dde254e9b9b98ac81dcbcf7a5b832","target":"record","created_at":"2026-07-16T01:22:35Z","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":"d77a537488750603642b62b7e3a30490615c21b4b21487eec1b0ec52374e5d5f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-03-03T17:42:42Z","title_canon_sha256":"d8b16420e7b46cffb37d23864879f1fe8c92aff9d3b753b28f77896bb40a8094"},"schema_version":"1.0","source":{"id":"2603.03183","kind":"arxiv","version":2}},"canonical_sha256":"2c199c105231bc133f8171fb93054b8f069e2cedf4bcf5323f76d56785ac632e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c199c105231bc133f8171fb93054b8f069e2cedf4bcf5323f76d56785ac632e","first_computed_at":"2026-07-16T01:22:35.513054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:35.513054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yn1Uo3ywr8p6RDnbEjiWORjEcbmtOa+EVh/taCohqqFr9GjiKg2BjRo+eJRjkYBxbqpENYT5MK+xmJvFUiwFBQ==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:35.513978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.03183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29390a193fe4b01999706a0e89fa970525dde254e9b9b98ac81dcbcf7a5b832","sha256:f068f0cf9e8d2bb71f1ae45d00f014ee7a8596844724c20d6e502f6d0b4aca20"],"state_sha256":"7271a1d92774f7e571497a65b62d5217498b92ba1bd7e5cafbb7aa692294af0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q2i49jwzYv21/d0a/oOh00vWeVpCO6gj/KQR+8fnzFwsDOLP+9xUVLAR/toOUgnQse2Ef6IvTYkg6F3sK+SxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T00:26:06.172781Z","bundle_sha256":"87763d455e5f5414c9e8db7ff58c5431ae9e12270fd808cb564f446de1ff57a2"}}