{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PP6C2ES4BCLKIVPKPRPPCHQUUL","short_pith_number":"pith:PP6C2ES4","canonical_record":{"source":{"id":"1605.08431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-26T19:52:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c19396091215b62866bf09f296de01fbead63eefb69057cc8933adee272cdd02","abstract_canon_sha256":"28ab08d6925fa1c6a3497db364b6da4b08e33fa48ba64e5711941799c671c41f"},"schema_version":"1.0"},"canonical_sha256":"7bfc2d125c0896a455ea7c5ef11e14a2f1b93a1d114fe0c13beff4486bd9c1d7","source":{"kind":"arxiv","id":"1605.08431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08431","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08431v1","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08431","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"PP6C2ES4BCLK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PP6C2ES4BCLKIVPK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PP6C2ES4","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PP6C2ES4BCLKIVPKPRPPCHQUUL","target":"record","payload":{"canonical_record":{"source":{"id":"1605.08431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-26T19:52:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c19396091215b62866bf09f296de01fbead63eefb69057cc8933adee272cdd02","abstract_canon_sha256":"28ab08d6925fa1c6a3497db364b6da4b08e33fa48ba64e5711941799c671c41f"},"schema_version":"1.0"},"canonical_sha256":"7bfc2d125c0896a455ea7c5ef11e14a2f1b93a1d114fe0c13beff4486bd9c1d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:34.335638Z","signature_b64":"AVnzjozCSAoPbjctNPecvKRngGV/dzxKRyAWatngDqX844E4CzyfWwaigE5WlkJzRuaN9rhucHsXwnPDHisrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfc2d125c0896a455ea7c5ef11e14a2f1b93a1d114fe0c13beff4486bd9c1d7","last_reissued_at":"2026-05-18T01:09:34.335204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:34.335204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.08431","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":"2026-05-18T01:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ThjN2QtBIw+Y4pKJ1MpQoj4x6io4OQH6xXteoSdpvkZnaMn/3zEk4ogNI5/Th4frasdqlayqmLGkaXyjqbolCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:33:51.167771Z"},"content_sha256":"990ba77cb28cc38b77fb3acb0d8e640bc7eaca3f7e5b078109f8669c5aca1c62","schema_version":"1.0","event_id":"sha256:990ba77cb28cc38b77fb3acb0d8e640bc7eaca3f7e5b078109f8669c5aca1c62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PP6C2ES4BCLKIVPKPRPPCHQUUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Polynomial Form of the Scattering Equations is an H-Basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jorrit Bosma, Mads Sogaard, Yang Zhang","submitted_at":"2016-05-26T19:52:12Z","abstract_excerpt":"We prove that the polynomial form of the scattering equations is a Macaulay H-basis. We demonstrate that this H-basis facilitates integrand reduction and global residue computations in a way very similar to using a Gr\\\"obner basis, but circumvents the heavy computation of the latter. As an example, we apply the H-basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08431","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":""},"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":"2026-05-18T01:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VEka7ljE7Ohja34SwoHCe/oMnkZYYaHk7PMANW0TNAyTL9+YhD2yUCdB/ggwT/G+aEKmbIqfA4Fzl3QKTn4eCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:33:51.168498Z"},"content_sha256":"f3c506504d9e8a05f9ca91b0493f6e073e16565e70e591ec186316396ac45a0d","schema_version":"1.0","event_id":"sha256:f3c506504d9e8a05f9ca91b0493f6e073e16565e70e591ec186316396ac45a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/bundle.json","state_url":"https://pith.science/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/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":"2026-06-11T23:33:51Z","links":{"resolver":"https://pith.science/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL","bundle":"https://pith.science/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/bundle.json","state":"https://pith.science/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PP6C2ES4BCLKIVPKPRPPCHQUUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PP6C2ES4BCLKIVPKPRPPCHQUUL","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":"28ab08d6925fa1c6a3497db364b6da4b08e33fa48ba64e5711941799c671c41f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-26T19:52:12Z","title_canon_sha256":"c19396091215b62866bf09f296de01fbead63eefb69057cc8933adee272cdd02"},"schema_version":"1.0","source":{"id":"1605.08431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08431","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08431v1","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08431","created_at":"2026-05-18T01:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"PP6C2ES4BCLK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PP6C2ES4BCLKIVPK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PP6C2ES4","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:f3c506504d9e8a05f9ca91b0493f6e073e16565e70e591ec186316396ac45a0d","target":"graph","created_at":"2026-05-18T01:09:34Z","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"},"paper":{"abstract_excerpt":"We prove that the polynomial form of the scattering equations is a Macaulay H-basis. We demonstrate that this H-basis facilitates integrand reduction and global residue computations in a way very similar to using a Gr\\\"obner basis, but circumvents the heavy computation of the latter. As an example, we apply the H-basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term.","authors_text":"Jorrit Bosma, Mads Sogaard, Yang Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-26T19:52:12Z","title":"The Polynomial Form of the Scattering Equations is an H-Basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08431","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":"sha256:990ba77cb28cc38b77fb3acb0d8e640bc7eaca3f7e5b078109f8669c5aca1c62","target":"record","created_at":"2026-05-18T01:09:34Z","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":"28ab08d6925fa1c6a3497db364b6da4b08e33fa48ba64e5711941799c671c41f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-26T19:52:12Z","title_canon_sha256":"c19396091215b62866bf09f296de01fbead63eefb69057cc8933adee272cdd02"},"schema_version":"1.0","source":{"id":"1605.08431","kind":"arxiv","version":1}},"canonical_sha256":"7bfc2d125c0896a455ea7c5ef11e14a2f1b93a1d114fe0c13beff4486bd9c1d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bfc2d125c0896a455ea7c5ef11e14a2f1b93a1d114fe0c13beff4486bd9c1d7","first_computed_at":"2026-05-18T01:09:34.335204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:34.335204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVnzjozCSAoPbjctNPecvKRngGV/dzxKRyAWatngDqX844E4CzyfWwaigE5WlkJzRuaN9rhucHsXwnPDHisrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:34.335638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:990ba77cb28cc38b77fb3acb0d8e640bc7eaca3f7e5b078109f8669c5aca1c62","sha256:f3c506504d9e8a05f9ca91b0493f6e073e16565e70e591ec186316396ac45a0d"],"state_sha256":"d05f624159eae48317fa9e12140e777c75fab5d688e191c54d7ca95a7d74a465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yTAX7Qf2Pm2vxS28kyytD/Q9/QK1s0/tJpQ5Db97RM+WjxUEK1u/F0ZW4Zhbs0lMSziASQXtQQd705p6wgSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:33:51.178456Z","bundle_sha256":"6fd9576eacad0ec81e195e0fed95a716c27c1fdabfb76802fa804648c936280d"}}