{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:NWW3Q5FKJ5VYPVTTWBTD2SYW4H","short_pith_number":"pith:NWW3Q5FK","schema_version":"1.0","canonical_sha256":"6dadb874aa4f6b87d673b0663d4b16e1f92a83be647225e3b0a9bd0ea52aa879","source":{"kind":"arxiv","id":"0903.2101","version":2},"attestation_state":"computed","paper":{"title":"Combinatorial Deformations of Algebras: Twisting and Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"cs.SC","authors_text":"Christophe Tollu (LIPN), G\\'erard Henry Edmond Duchamp (LIPN), Gleb Koshevoy (CEMI), K. A. Penson (LPTMC)","submitted_at":"2009-03-12T06:12:32Z","abstract_excerpt":"The framework used to prove the multiplicative law deformation of the algebra of Feynman-Bender diagrams is a \\textit{twisted shifted dual law} (in fact, twice). We give here a clear interpretation of its two parameters. The crossing parameter is a deformation of the tensor structure whereas the superposition parameters is a perturbation of the shuffle coproduct of Hoffman type which, in turn, can be interpreted as the diagonal restriction of a superproduct. Here, we systematically detail these constructions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0903.2101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-03-12T06:12:32Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"ae12efaf2b2684955d4a066bc27e32df894f4cc72f3a48368eba9853c0aec622","abstract_canon_sha256":"2c4f8fd4893022a84e8b9a439b15dd04752271df018800d60777a62554441c59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:44.947541Z","signature_b64":"Iw6ukQ9JMbL6ChFH2qKww5L7qj8GyY5hwXDvK0wDP0zFPbL96xKA12PesUiN4nkBBgMzT9tjR4bwt2ydTbPNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dadb874aa4f6b87d673b0663d4b16e1f92a83be647225e3b0a9bd0ea52aa879","last_reissued_at":"2026-05-18T04:41:44.947124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:44.947124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Deformations of Algebras: Twisting and Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"cs.SC","authors_text":"Christophe Tollu (LIPN), G\\'erard Henry Edmond Duchamp (LIPN), Gleb Koshevoy (CEMI), K. A. Penson (LPTMC)","submitted_at":"2009-03-12T06:12:32Z","abstract_excerpt":"The framework used to prove the multiplicative law deformation of the algebra of Feynman-Bender diagrams is a \\textit{twisted shifted dual law} (in fact, twice). We give here a clear interpretation of its two parameters. The crossing parameter is a deformation of the tensor structure whereas the superposition parameters is a perturbation of the shuffle coproduct of Hoffman type which, in turn, can be interpreted as the diagonal restriction of a superproduct. Here, we systematically detail these constructions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2101","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0903.2101","created_at":"2026-05-18T04:41:44.947195+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.2101v2","created_at":"2026-05-18T04:41:44.947195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.2101","created_at":"2026-05-18T04:41:44.947195+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWW3Q5FKJ5VY","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWW3Q5FKJ5VYPVTT","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWW3Q5FK","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H","json":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H.json","graph_json":"https://pith.science/api/pith-number/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/graph.json","events_json":"https://pith.science/api/pith-number/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/events.json","paper":"https://pith.science/paper/NWW3Q5FK"},"agent_actions":{"view_html":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H","download_json":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H.json","view_paper":"https://pith.science/paper/NWW3Q5FK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.2101&json=true","fetch_graph":"https://pith.science/api/pith-number/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/graph.json","fetch_events":"https://pith.science/api/pith-number/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/action/storage_attestation","attest_author":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/action/author_attestation","sign_citation":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/action/citation_signature","submit_replication":"https://pith.science/pith/NWW3Q5FKJ5VYPVTTWBTD2SYW4H/action/replication_record"}},"created_at":"2026-05-18T04:41:44.947195+00:00","updated_at":"2026-05-18T04:41:44.947195+00:00"}