{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CLRSSN3VVT7KTE7BZL4LIYXAIF","short_pith_number":"pith:CLRSSN3V","schema_version":"1.0","canonical_sha256":"12e3293775acfea993e1caf8b462e0414de1af4bcac73e6bc32996352f663535","source":{"kind":"arxiv","id":"1507.01089","version":2},"attestation_state":"computed","paper":{"title":"(Pure) transcendence bases in $\\phi$-deformed shuffle bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.GR","math.MP"],"primary_cat":"cs.SC","authors_text":"Christophe Tollu (LIPN), G\\'erard H.E. Duchamp (LIPN), Quoc Hoan Ng\\^o (LIPN), Van Chi\\^en Bui (LIPN), Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2015-07-04T09:25:07Z","abstract_excerpt":"Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform act on a bialgebra isomorphic to an enveloping algebra. That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincar\\'e--Birkhoff--Witt bases. In this paper, we systematically study these deformations, obtaining necessary and sufficient conditions for the operators to exist, and we"},"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":"1507.01089","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-07-04T09:25:07Z","cross_cats_sorted":["math-ph","math.CO","math.GR","math.MP"],"title_canon_sha256":"4186792308a08f8212fde4616dea410ddff74f7b890d5a6f4398b2c67390c394","abstract_canon_sha256":"6ae53065d52c1d859c7a915352f6bfa551b7c2db4392860848403f593a3c85ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:50.995090Z","signature_b64":"VY5rojuvv42YWe7E6No7FRFf2AncCR7NmpOkCmPO4t0dN7HzWeL9ynArL7rUDxvhAskvp8MXiAhhaFYHaSCGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12e3293775acfea993e1caf8b462e0414de1af4bcac73e6bc32996352f663535","last_reissued_at":"2026-05-18T00:12:50.994603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:50.994603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"(Pure) transcendence bases in $\\phi$-deformed shuffle bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.GR","math.MP"],"primary_cat":"cs.SC","authors_text":"Christophe Tollu (LIPN), G\\'erard H.E. Duchamp (LIPN), Quoc Hoan Ng\\^o (LIPN), Van Chi\\^en Bui (LIPN), Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2015-07-04T09:25:07Z","abstract_excerpt":"Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform act on a bialgebra isomorphic to an enveloping algebra. That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincar\\'e--Birkhoff--Witt bases. In this paper, we systematically study these deformations, obtaining necessary and sufficient conditions for the operators to exist, and we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01089","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":"1507.01089","created_at":"2026-05-18T00:12:50.994672+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01089v2","created_at":"2026-05-18T00:12:50.994672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01089","created_at":"2026-05-18T00:12:50.994672+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLRSSN3VVT7K","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLRSSN3VVT7KTE7B","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLRSSN3V","created_at":"2026-05-18T12:29:17.054201+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/CLRSSN3VVT7KTE7BZL4LIYXAIF","json":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF.json","graph_json":"https://pith.science/api/pith-number/CLRSSN3VVT7KTE7BZL4LIYXAIF/graph.json","events_json":"https://pith.science/api/pith-number/CLRSSN3VVT7KTE7BZL4LIYXAIF/events.json","paper":"https://pith.science/paper/CLRSSN3V"},"agent_actions":{"view_html":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF","download_json":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF.json","view_paper":"https://pith.science/paper/CLRSSN3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01089&json=true","fetch_graph":"https://pith.science/api/pith-number/CLRSSN3VVT7KTE7BZL4LIYXAIF/graph.json","fetch_events":"https://pith.science/api/pith-number/CLRSSN3VVT7KTE7BZL4LIYXAIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF/action/storage_attestation","attest_author":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF/action/author_attestation","sign_citation":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF/action/citation_signature","submit_replication":"https://pith.science/pith/CLRSSN3VVT7KTE7BZL4LIYXAIF/action/replication_record"}},"created_at":"2026-05-18T00:12:50.994672+00:00","updated_at":"2026-05-18T00:12:50.994672+00:00"}