{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HY35DYO62AMFWGRTK7Q2E6H26H","short_pith_number":"pith:HY35DYO6","canonical_record":{"source":{"id":"2606.28052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-26T12:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"7dbf3ebeadcdaf83ddf403e3383b155888aebc3e0d6b3554fc36f7375a14f137","abstract_canon_sha256":"3807c5ed536e7188def89826c87091054bfcb2bde8221c5f5faaa39e8dc5d113"},"schema_version":"1.0"},"canonical_sha256":"3e37d1e1ded0185b1a3357e1a278faf1c408054a415f7b9f09e32825b070d631","source":{"kind":"arxiv","id":"2606.28052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28052","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28052v1","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28052","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"HY35DYO62AMF","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_16","alias_value":"HY35DYO62AMFWGRT","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_8","alias_value":"HY35DYO6","created_at":"2026-06-29T01:14:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HY35DYO62AMFWGRTK7Q2E6H26H","target":"record","payload":{"canonical_record":{"source":{"id":"2606.28052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-26T12:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"7dbf3ebeadcdaf83ddf403e3383b155888aebc3e0d6b3554fc36f7375a14f137","abstract_canon_sha256":"3807c5ed536e7188def89826c87091054bfcb2bde8221c5f5faaa39e8dc5d113"},"schema_version":"1.0"},"canonical_sha256":"3e37d1e1ded0185b1a3357e1a278faf1c408054a415f7b9f09e32825b070d631","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:14:56.371487Z","signature_b64":"D79fItj04hoa+22pO6vd/mlrlpyffhjuzkJ5GGFGU18CIGlUlxsXzLeXJUd556LTurhdo2rNhN7pmvBeSoZjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e37d1e1ded0185b1a3357e1a278faf1c408054a415f7b9f09e32825b070d631","last_reissued_at":"2026-06-29T01:14:56.371025Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:14:56.371025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.28052","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":"2026-06-29T01:14:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5U/uScEK1xMAURswrViF30fY78yYdsjPje7JaqX//xIwIyQKkyLYfOccC+ZbCCGF98DgrmGP/ZeoLHIXqreCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:32:13.904228Z"},"content_sha256":"1e6db331f074dfe851716f419c568f6c180b0390d76c713fd3a698e825a22437","schema_version":"1.0","event_id":"sha256:1e6db331f074dfe851716f419c568f6c180b0390d76c713fd3a698e825a22437"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HY35DYO62AMFWGRTK7Q2E6H26H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Planar loop integrands from cuts in $D$ dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Fan Zhu, Song He, Zhenqi Han","submitted_at":"2026-06-26T12:54:29Z","abstract_excerpt":"We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal M\\\"obius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28052","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/2606.28052/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":"2026-06-29T01:14:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDO80TzkWzYSgfk+FM+PligcKaLZihy5InogcliZlh5ugZRqqcgO1R1KhadhITbW69mDhfDuF/VfZ0kB7u3SBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:32:13.904748Z"},"content_sha256":"02eec03570c01b8950974027277131fc092c196d023a48dcd2c664bdc341dc27","schema_version":"1.0","event_id":"sha256:02eec03570c01b8950974027277131fc092c196d023a48dcd2c664bdc341dc27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY35DYO62AMFWGRTK7Q2E6H26H/bundle.json","state_url":"https://pith.science/pith/HY35DYO62AMFWGRTK7Q2E6H26H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY35DYO62AMFWGRTK7Q2E6H26H/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":"2026-06-29T22:32:13Z","links":{"resolver":"https://pith.science/pith/HY35DYO62AMFWGRTK7Q2E6H26H","bundle":"https://pith.science/pith/HY35DYO62AMFWGRTK7Q2E6H26H/bundle.json","state":"https://pith.science/pith/HY35DYO62AMFWGRTK7Q2E6H26H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY35DYO62AMFWGRTK7Q2E6H26H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HY35DYO62AMFWGRTK7Q2E6H26H","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":"3807c5ed536e7188def89826c87091054bfcb2bde8221c5f5faaa39e8dc5d113","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-26T12:54:29Z","title_canon_sha256":"7dbf3ebeadcdaf83ddf403e3383b155888aebc3e0d6b3554fc36f7375a14f137"},"schema_version":"1.0","source":{"id":"2606.28052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28052","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28052v1","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28052","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"HY35DYO62AMF","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_16","alias_value":"HY35DYO62AMFWGRT","created_at":"2026-06-29T01:14:56Z"},{"alias_kind":"pith_short_8","alias_value":"HY35DYO6","created_at":"2026-06-29T01:14:56Z"}],"graph_snapshots":[{"event_id":"sha256:02eec03570c01b8950974027277131fc092c196d023a48dcd2c664bdc341dc27","target":"graph","created_at":"2026-06-29T01:14:56Z","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/2606.28052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal M\\\"obius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes","authors_text":"Fan Zhu, Song He, Zhenqi Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-26T12:54:29Z","title":"Planar loop integrands from cuts in $D$ dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28052","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":"sha256:1e6db331f074dfe851716f419c568f6c180b0390d76c713fd3a698e825a22437","target":"record","created_at":"2026-06-29T01:14:56Z","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":"3807c5ed536e7188def89826c87091054bfcb2bde8221c5f5faaa39e8dc5d113","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-26T12:54:29Z","title_canon_sha256":"7dbf3ebeadcdaf83ddf403e3383b155888aebc3e0d6b3554fc36f7375a14f137"},"schema_version":"1.0","source":{"id":"2606.28052","kind":"arxiv","version":1}},"canonical_sha256":"3e37d1e1ded0185b1a3357e1a278faf1c408054a415f7b9f09e32825b070d631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e37d1e1ded0185b1a3357e1a278faf1c408054a415f7b9f09e32825b070d631","first_computed_at":"2026-06-29T01:14:56.371025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:14:56.371025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D79fItj04hoa+22pO6vd/mlrlpyffhjuzkJ5GGFGU18CIGlUlxsXzLeXJUd556LTurhdo2rNhN7pmvBeSoZjBg==","signature_status":"signed_v1","signed_at":"2026-06-29T01:14:56.371487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e6db331f074dfe851716f419c568f6c180b0390d76c713fd3a698e825a22437","sha256:02eec03570c01b8950974027277131fc092c196d023a48dcd2c664bdc341dc27"],"state_sha256":"ca9235cec4641a882a7057b59cc7a2a263b75675d91eec25e1a33e19dc4af1ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNqMuwl0IhD8H+R4yi6mpsQD+TD4Fgf14P4zlUuTDht1rhgrN1W432dw41jhCxfsE//3WUYEnR+T3HYuxsk4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T22:32:13.907377Z","bundle_sha256":"06bbdadb4988c448587390426012b273887284c2b96348ff6f1bd3bcc6b6786f"}}