{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:E4Z5RPN4YYTEHFUTVQ2Z47433F","short_pith_number":"pith:E4Z5RPN4","canonical_record":{"source":{"id":"2512.15882","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-17T19:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"696a2eb10e218fa8c849b894b1b2ba7b018bb0c9110a68b69516a3d9d0f50f8e","abstract_canon_sha256":"565802f4c69c6f7fbac84658f7b1aa9c7f6d34203194bc9575fed37c8963a037"},"schema_version":"1.0"},"canonical_sha256":"2733d8bdbcc626439693ac359e7f9bd943aef7016821e88f7fc7f8e6e7e30f84","source":{"kind":"arxiv","id":"2512.15882","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.15882","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"2512.15882v2","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.15882","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"E4Z5RPN4YYTE","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_16","alias_value":"E4Z5RPN4YYTEHFUT","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_8","alias_value":"E4Z5RPN4","created_at":"2026-07-21T01:19:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:E4Z5RPN4YYTEHFUTVQ2Z47433F","target":"record","payload":{"canonical_record":{"source":{"id":"2512.15882","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-17T19:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"696a2eb10e218fa8c849b894b1b2ba7b018bb0c9110a68b69516a3d9d0f50f8e","abstract_canon_sha256":"565802f4c69c6f7fbac84658f7b1aa9c7f6d34203194bc9575fed37c8963a037"},"schema_version":"1.0"},"canonical_sha256":"2733d8bdbcc626439693ac359e7f9bd943aef7016821e88f7fc7f8e6e7e30f84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:19:51.459163Z","signature_b64":"61l+aJFLeNdxLhnz9MWRE2vbnMk14y0mp4HDBGUf6QEFdom796hjf2CtpTzELcK/9eITbQMNwmFsFUrFFTjCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2733d8bdbcc626439693ac359e7f9bd943aef7016821e88f7fc7f8e6e7e30f84","last_reissued_at":"2026-07-21T01:19:51.458196Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:19:51.458196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.15882","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":"2026-07-21T01:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHmn/UCezAZmYvqQjf/s/GIWS8xwKgmip9RfKq36yccTZfOPs9a6yCxg9kFvkFMpNcMNRjTSyHSXI9QA3vwLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:02:44.736149Z"},"content_sha256":"905aad98e194066c9d0e268e94457e658355870c98be7d9039c84a37dcf97992","schema_version":"1.0","event_id":"sha256:905aad98e194066c9d0e268e94457e658355870c98be7d9039c84a37dcf97992"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:E4Z5RPN4YYTEHFUTVQ2Z47433F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On differential operators for scalar-scaffolded gluons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dongyu Yang, Jin Dong, Yong-Xiang Su","submitted_at":"2025-12-17T19:00:38Z","abstract_excerpt":"Recently, based on the curve-integral formulation for stringy Tr$\\phi^3$ amplitudes, a combinatorial formulation for Yang-Mills amplitudes has been proposed which describes gluons using pairs of scalars and produces the $n$-gluon amplitude from simple kinematical shift of stringy Tr$\\phi^3$ amplitudes with $2n$ scalars. It has revealed a variety of new properties and structures even for tree-level gluon amplitudes such as hidden zeros and splits, and in this note we provide another example: we study differential operators acting on Yang-Mills amplitudes with respect to $2n$-scalar kinematic va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.15882","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/2512.15882/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":"2026-07-21T01:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KFXfgLJXhVUI9XpGqWoG+oLrp+JaLedDXcUE0v2k6evzaDNGn3x9f+zYqrmSQpQHY8hhHGnofe7YArrhfxaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:02:44.736666Z"},"content_sha256":"e5efaed1b20236604729f88bdf6c7969a2e97f020d3c05fc9a7d77a34b31d08f","schema_version":"1.0","event_id":"sha256:e5efaed1b20236604729f88bdf6c7969a2e97f020d3c05fc9a7d77a34b31d08f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/bundle.json","state_url":"https://pith.science/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/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":"2026-08-05T04:02:44Z","links":{"resolver":"https://pith.science/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F","bundle":"https://pith.science/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/bundle.json","state":"https://pith.science/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4Z5RPN4YYTEHFUTVQ2Z47433F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:E4Z5RPN4YYTEHFUTVQ2Z47433F","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":"565802f4c69c6f7fbac84658f7b1aa9c7f6d34203194bc9575fed37c8963a037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-17T19:00:38Z","title_canon_sha256":"696a2eb10e218fa8c849b894b1b2ba7b018bb0c9110a68b69516a3d9d0f50f8e"},"schema_version":"1.0","source":{"id":"2512.15882","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.15882","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"2512.15882v2","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.15882","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"E4Z5RPN4YYTE","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_16","alias_value":"E4Z5RPN4YYTEHFUT","created_at":"2026-07-21T01:19:51Z"},{"alias_kind":"pith_short_8","alias_value":"E4Z5RPN4","created_at":"2026-07-21T01:19:51Z"}],"graph_snapshots":[{"event_id":"sha256:e5efaed1b20236604729f88bdf6c7969a2e97f020d3c05fc9a7d77a34b31d08f","target":"graph","created_at":"2026-07-21T01:19:51Z","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/2512.15882/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, based on the curve-integral formulation for stringy Tr$\\phi^3$ amplitudes, a combinatorial formulation for Yang-Mills amplitudes has been proposed which describes gluons using pairs of scalars and produces the $n$-gluon amplitude from simple kinematical shift of stringy Tr$\\phi^3$ amplitudes with $2n$ scalars. It has revealed a variety of new properties and structures even for tree-level gluon amplitudes such as hidden zeros and splits, and in this note we provide another example: we study differential operators acting on Yang-Mills amplitudes with respect to $2n$-scalar kinematic va","authors_text":"Dongyu Yang, Jin Dong, Yong-Xiang Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-17T19:00:38Z","title":"On differential operators for scalar-scaffolded gluons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.15882","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":"sha256:905aad98e194066c9d0e268e94457e658355870c98be7d9039c84a37dcf97992","target":"record","created_at":"2026-07-21T01:19:51Z","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":"565802f4c69c6f7fbac84658f7b1aa9c7f6d34203194bc9575fed37c8963a037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-17T19:00:38Z","title_canon_sha256":"696a2eb10e218fa8c849b894b1b2ba7b018bb0c9110a68b69516a3d9d0f50f8e"},"schema_version":"1.0","source":{"id":"2512.15882","kind":"arxiv","version":2}},"canonical_sha256":"2733d8bdbcc626439693ac359e7f9bd943aef7016821e88f7fc7f8e6e7e30f84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2733d8bdbcc626439693ac359e7f9bd943aef7016821e88f7fc7f8e6e7e30f84","first_computed_at":"2026-07-21T01:19:51.458196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:19:51.458196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61l+aJFLeNdxLhnz9MWRE2vbnMk14y0mp4HDBGUf6QEFdom796hjf2CtpTzELcK/9eITbQMNwmFsFUrFFTjCBw==","signature_status":"signed_v1","signed_at":"2026-07-21T01:19:51.459163Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.15882","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:905aad98e194066c9d0e268e94457e658355870c98be7d9039c84a37dcf97992","sha256:e5efaed1b20236604729f88bdf6c7969a2e97f020d3c05fc9a7d77a34b31d08f"],"state_sha256":"8b0887133453418b3c52b9cc63494cdd49443b345d0cd19cd71a1225e09a142b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLnPqxtVwjjO8yiQnJWK4Z7o7QpBdaLLgAn+fso2x+ConRV6ux4mQcIEk48mVfVZ7F7vAvoTnoIvbPDZaeDGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:02:44.740937Z","bundle_sha256":"619bf9f2a6b21d605e827c8dab59383c3c6c5ad8a85b8d3b2497d4d96d89268f"}}