{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NQP7KZDWF7I64TH46763BGSYBI","short_pith_number":"pith:NQP7KZDW","schema_version":"1.0","canonical_sha256":"6c1ff564762fd1ee4cfcf7fdb09a580a00ea58007819dcd1950b509f8fe63535","source":{"kind":"arxiv","id":"1511.06859","version":1},"attestation_state":"computed","paper":{"title":"Mulitgraded Dyson-Schwinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Lo\\\"ic Foissy (LMPA)","submitted_at":"2015-11-21T09:31:43Z","abstract_excerpt":"We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number $N$ of coupling constants. The considered Hopf algebra of Feynman graphs is $\\mathbb{N}^N$-graded, and we wonder if the graded subalgebra generated by the solution is Hopf or not. We first introduce a family of pre-Lie algebras which we classify, dually providing systems generating a Hopf subalgebra, we also describe the associated groups, as extensions of groups of formal diffeomorphisms on several variables. We then consider systems coming from Feynman graphs of a Quantum Field Theory.  We show that if the n"},"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":"1511.06859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-21T09:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"5377b288b7b7b3b947cc23eba37a4e4874812189ba5980b85a6a550f5ec13737","abstract_canon_sha256":"3617444aeabac7a438dde94f909c4d60e061d1a204fe751e4f186f40e847d764"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:17.329735Z","signature_b64":"/LbRoz1kMQeo5YsgePNmG+qfg4VR4JLopqtAoe7XRq+De8n0FIn8pGSuoVcQbaSlOp3Xl1W0O616a+m+hB87Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c1ff564762fd1ee4cfcf7fdb09a580a00ea58007819dcd1950b509f8fe63535","last_reissued_at":"2026-05-18T01:26:17.329238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:17.329238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mulitgraded Dyson-Schwinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Lo\\\"ic Foissy (LMPA)","submitted_at":"2015-11-21T09:31:43Z","abstract_excerpt":"We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number $N$ of coupling constants. The considered Hopf algebra of Feynman graphs is $\\mathbb{N}^N$-graded, and we wonder if the graded subalgebra generated by the solution is Hopf or not. We first introduce a family of pre-Lie algebras which we classify, dually providing systems generating a Hopf subalgebra, we also describe the associated groups, as extensions of groups of formal diffeomorphisms on several variables. We then consider systems coming from Feynman graphs of a Quantum Field Theory.  We show that if the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06859","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.06859","created_at":"2026-05-18T01:26:17.329331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06859v1","created_at":"2026-05-18T01:26:17.329331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06859","created_at":"2026-05-18T01:26:17.329331+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQP7KZDWF7I6","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQP7KZDWF7I64TH4","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQP7KZDW","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.12350","citing_title":"The algebraic structure of Dyson--Schwinger equations with multiple insertion places","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI","json":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI.json","graph_json":"https://pith.science/api/pith-number/NQP7KZDWF7I64TH46763BGSYBI/graph.json","events_json":"https://pith.science/api/pith-number/NQP7KZDWF7I64TH46763BGSYBI/events.json","paper":"https://pith.science/paper/NQP7KZDW"},"agent_actions":{"view_html":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI","download_json":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI.json","view_paper":"https://pith.science/paper/NQP7KZDW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06859&json=true","fetch_graph":"https://pith.science/api/pith-number/NQP7KZDWF7I64TH46763BGSYBI/graph.json","fetch_events":"https://pith.science/api/pith-number/NQP7KZDWF7I64TH46763BGSYBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI/action/storage_attestation","attest_author":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI/action/author_attestation","sign_citation":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI/action/citation_signature","submit_replication":"https://pith.science/pith/NQP7KZDWF7I64TH46763BGSYBI/action/replication_record"}},"created_at":"2026-05-18T01:26:17.329331+00:00","updated_at":"2026-05-18T01:26:17.329331+00:00"}