{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SJ3BBJJBS66XI2DNWBP5GEDFH2","short_pith_number":"pith:SJ3BBJJB","canonical_record":{"source":{"id":"1104.3415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-18T09:14:06Z","cross_cats_sorted":["hep-th","math.MP","math.RA"],"title_canon_sha256":"f8df7f17fbf084d0768005ddc204b8b56e951744297ad8123ab87d7573638bf5","abstract_canon_sha256":"5f06069de0698d2c2fc57da381a56ab710f7e168379fd00aaa97f78f94fca9db"},"schema_version":"1.0"},"canonical_sha256":"927610a52197bd74686db05fd310653ea9d5e6d2ce7c90d0b96ca9611093dc90","source":{"kind":"arxiv","id":"1104.3415","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3415","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3415v2","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3415","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"SJ3BBJJBS66X","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SJ3BBJJBS66XI2DN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SJ3BBJJB","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SJ3BBJJBS66XI2DNWBP5GEDFH2","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-18T09:14:06Z","cross_cats_sorted":["hep-th","math.MP","math.RA"],"title_canon_sha256":"f8df7f17fbf084d0768005ddc204b8b56e951744297ad8123ab87d7573638bf5","abstract_canon_sha256":"5f06069de0698d2c2fc57da381a56ab710f7e168379fd00aaa97f78f94fca9db"},"schema_version":"1.0"},"canonical_sha256":"927610a52197bd74686db05fd310653ea9d5e6d2ce7c90d0b96ca9611093dc90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:39.967178Z","signature_b64":"EAkA+VngoU4MplO0OJvRifZa7UM4rLEi/Of4tSwgrqPwMYkrVxcFIb7Lx+uET7nFj3Tr0MqHEXn7M62gy9zIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"927610a52197bd74686db05fd310653ea9d5e6d2ce7c90d0b96ca9611093dc90","last_reissued_at":"2026-05-18T01:55:39.966480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:39.966480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3415","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dgA4InEcuAcK+fDfarmBa3bHW22wrt4wIsfHthGxFnk78S9ZYCAIbyNmZgLRyaX4H/Q1pAZcAsHUFNl1Ju1FAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:57:19.275607Z"},"content_sha256":"c7f43643cf812d42b339efea19f0cf96693a4be9b991afd589fe5624feed7a81","schema_version":"1.0","event_id":"sha256:c7f43643cf812d42b339efea19f0cf96693a4be9b991afd589fe5624feed7a81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SJ3BBJJBS66XI2DNWBP5GEDFH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Frederic Patras, Kurusch Ebrahimi-Fard","submitted_at":"2011-04-18T09:14:06Z","abstract_excerpt":"This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the pecul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3415","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFYrf4uMTlze0XuOsw34EN4jzk3rtDf4BBKDVUSSNhfzGTV3PwwfEk1kmQwaTvw+QLH+K+2QXC6Ka/cCwfmJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:57:19.275995Z"},"content_sha256":"3376b947b0574de2ef62044f859484e6c540961c9d899dd10bc4891e31d887d3","schema_version":"1.0","event_id":"sha256:3376b947b0574de2ef62044f859484e6c540961c9d899dd10bc4891e31d887d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/bundle.json","state_url":"https://pith.science/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/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":"2026-05-30T20:57:19Z","links":{"resolver":"https://pith.science/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2","bundle":"https://pith.science/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/bundle.json","state":"https://pith.science/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJ3BBJJBS66XI2DNWBP5GEDFH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SJ3BBJJBS66XI2DNWBP5GEDFH2","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":"5f06069de0698d2c2fc57da381a56ab710f7e168379fd00aaa97f78f94fca9db","cross_cats_sorted":["hep-th","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-18T09:14:06Z","title_canon_sha256":"f8df7f17fbf084d0768005ddc204b8b56e951744297ad8123ab87d7573638bf5"},"schema_version":"1.0","source":{"id":"1104.3415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3415","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3415v2","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3415","created_at":"2026-05-18T01:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"SJ3BBJJBS66X","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SJ3BBJJBS66XI2DN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SJ3BBJJB","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:3376b947b0574de2ef62044f859484e6c540961c9d899dd10bc4891e31d887d3","target":"graph","created_at":"2026-05-18T01:55:39Z","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":"This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the pecul","authors_text":"Frederic Patras, Kurusch Ebrahimi-Fard","cross_cats":["hep-th","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-18T09:14:06Z","title":"Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3415","kind":"arxiv","version":2},"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:c7f43643cf812d42b339efea19f0cf96693a4be9b991afd589fe5624feed7a81","target":"record","created_at":"2026-05-18T01:55:39Z","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":"5f06069de0698d2c2fc57da381a56ab710f7e168379fd00aaa97f78f94fca9db","cross_cats_sorted":["hep-th","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-18T09:14:06Z","title_canon_sha256":"f8df7f17fbf084d0768005ddc204b8b56e951744297ad8123ab87d7573638bf5"},"schema_version":"1.0","source":{"id":"1104.3415","kind":"arxiv","version":2}},"canonical_sha256":"927610a52197bd74686db05fd310653ea9d5e6d2ce7c90d0b96ca9611093dc90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"927610a52197bd74686db05fd310653ea9d5e6d2ce7c90d0b96ca9611093dc90","first_computed_at":"2026-05-18T01:55:39.966480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:39.966480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EAkA+VngoU4MplO0OJvRifZa7UM4rLEi/Of4tSwgrqPwMYkrVxcFIb7Lx+uET7nFj3Tr0MqHEXn7M62gy9zIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:39.967178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f43643cf812d42b339efea19f0cf96693a4be9b991afd589fe5624feed7a81","sha256:3376b947b0574de2ef62044f859484e6c540961c9d899dd10bc4891e31d887d3"],"state_sha256":"ce0b5e4d7379261b7119a8e48d988ed8974df11e049e4eb0fd2ad5d47a8a4267"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qeh7DOF32wkwDthtRxvct6bAVQjZRoizjUmN8FxFzLRxELShx7OQwW9Xx3P3Zy634MzrtmHEVqSq9ri0Kx1HBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:57:19.278305Z","bundle_sha256":"447bd11d43805787cf91b44b05e1a5775a7d14d2598a5f0e05cfe28c2134b4a7"}}