{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MQ3UBFEHKNT4WNSC2ZBEFCMENS","short_pith_number":"pith:MQ3UBFEH","canonical_record":{"source":{"id":"1502.00147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T18:50:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e3bc94bfc711a889c5337f6498e9b7edc1115792da7a7ce32e3630228d43c478","abstract_canon_sha256":"4081b2cba719b13a83d7af527717718906246e9ca2f93f03dd2cb14c675813a1"},"schema_version":"1.0"},"canonical_sha256":"64374094875367cb3642d6424289846cac6a3b0202ff08a0914309032d5a49ea","source":{"kind":"arxiv","id":"1502.00147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00147","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00147v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00147","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"MQ3UBFEHKNT4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQ3UBFEHKNT4WNSC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQ3UBFEH","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MQ3UBFEHKNT4WNSC2ZBEFCMENS","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T18:50:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e3bc94bfc711a889c5337f6498e9b7edc1115792da7a7ce32e3630228d43c478","abstract_canon_sha256":"4081b2cba719b13a83d7af527717718906246e9ca2f93f03dd2cb14c675813a1"},"schema_version":"1.0"},"canonical_sha256":"64374094875367cb3642d6424289846cac6a3b0202ff08a0914309032d5a49ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.639540Z","signature_b64":"zVSq60MzHjratUklYKyku6hHK3JkkGAap6BIkD8tJcPT24+Fw38mzWpTLaazze+ZAp30Czu4Bi6/RT3w+bhIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64374094875367cb3642d6424289846cac6a3b0202ff08a0914309032d5a49ea","last_reissued_at":"2026-05-18T02:28:12.639117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.639117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00147","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZKkFxvDKXUA9ybwuICPHGW+dcXtO5c3psZXZsQPcK2qKLm2YdjevBuPNVIHw9X69Be9dKZ13vgjWUOrecEwzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:45:23.223966Z"},"content_sha256":"31e8159b06e3e4ddf8bd0f14ad5dd0f18b2a12747dc82155bbbc742cdf56e1e8","schema_version":"1.0","event_id":"sha256:31e8159b06e3e4ddf8bd0f14ad5dd0f18b2a12747dc82155bbbc742cdf56e1e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MQ3UBFEHKNT4WNSC2ZBEFCMENS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative version of Borcherds' approach to quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alessandra Frabetti (ICJ), Christian Brouder (IMPMC), Nguyen Viet Dang (LPP)","submitted_at":"2015-01-31T18:50:01Z","abstract_excerpt":"Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' quantization where the (external) tensor product plays the role of the normal product. We construct a noncommutative many-body Hopf algebra and a module over it which contains all the terms of the perturbative expansion and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00147","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/c8tIxVVpYLQpNQEG2mjGtV9yI99JpN5PimXvATZ8epeaFlJ3pwUXJvrvrVP1oH+oOG4Ej+Av9Zc/txJbJECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:45:23.224331Z"},"content_sha256":"625f83b94d3edb685764b4e50ba6506cc5ee43e7dfee98605970bba28cef7480","schema_version":"1.0","event_id":"sha256:625f83b94d3edb685764b4e50ba6506cc5ee43e7dfee98605970bba28cef7480"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/bundle.json","state_url":"https://pith.science/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/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":"2026-06-01T16:45:23Z","links":{"resolver":"https://pith.science/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS","bundle":"https://pith.science/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/bundle.json","state":"https://pith.science/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQ3UBFEHKNT4WNSC2ZBEFCMENS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MQ3UBFEHKNT4WNSC2ZBEFCMENS","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":"4081b2cba719b13a83d7af527717718906246e9ca2f93f03dd2cb14c675813a1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T18:50:01Z","title_canon_sha256":"e3bc94bfc711a889c5337f6498e9b7edc1115792da7a7ce32e3630228d43c478"},"schema_version":"1.0","source":{"id":"1502.00147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00147","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00147v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00147","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"MQ3UBFEHKNT4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQ3UBFEHKNT4WNSC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQ3UBFEH","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:625f83b94d3edb685764b4e50ba6506cc5ee43e7dfee98605970bba28cef7480","target":"graph","created_at":"2026-05-18T02:28:12Z","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":"Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' quantization where the (external) tensor product plays the role of the normal product. We construct a noncommutative many-body Hopf algebra and a module over it which contains all the terms of the perturbative expansion and","authors_text":"Alessandra Frabetti (ICJ), Christian Brouder (IMPMC), Nguyen Viet Dang (LPP)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T18:50:01Z","title":"Noncommutative version of Borcherds' approach to quantum field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00147","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":"sha256:31e8159b06e3e4ddf8bd0f14ad5dd0f18b2a12747dc82155bbbc742cdf56e1e8","target":"record","created_at":"2026-05-18T02:28:12Z","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":"4081b2cba719b13a83d7af527717718906246e9ca2f93f03dd2cb14c675813a1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T18:50:01Z","title_canon_sha256":"e3bc94bfc711a889c5337f6498e9b7edc1115792da7a7ce32e3630228d43c478"},"schema_version":"1.0","source":{"id":"1502.00147","kind":"arxiv","version":1}},"canonical_sha256":"64374094875367cb3642d6424289846cac6a3b0202ff08a0914309032d5a49ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64374094875367cb3642d6424289846cac6a3b0202ff08a0914309032d5a49ea","first_computed_at":"2026-05-18T02:28:12.639117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:12.639117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zVSq60MzHjratUklYKyku6hHK3JkkGAap6BIkD8tJcPT24+Fw38mzWpTLaazze+ZAp30Czu4Bi6/RT3w+bhIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:12.639540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31e8159b06e3e4ddf8bd0f14ad5dd0f18b2a12747dc82155bbbc742cdf56e1e8","sha256:625f83b94d3edb685764b4e50ba6506cc5ee43e7dfee98605970bba28cef7480"],"state_sha256":"deb2f675b15db62f3a2377c6e6fd3aebe53edc21671abfaecba70a5121be8071"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DN+3nXVIn8kiESfB+2cPZVyTz38QYG/RMH6hqG0cdPurkfo0UuBDBr/ftGeYcEz3TKmDAIHjudX7HDdNbZLdCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:45:23.226264Z","bundle_sha256":"59c34ad65672c31d09b2dbfda500ad71ec066a974eaa6f18e74340f478010811"}}