{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JC2FOATREAEY5KUSH2RTBTSKPR","short_pith_number":"pith:JC2FOATR","canonical_record":{"source":{"id":"1207.6321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-26T16:31:39Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"8025ff464ed9289cf399e5111ac065203291af1aa4dd6008d5bbd0d5bb9bc485","abstract_canon_sha256":"af432eea1802c005b7a7354d4fb3308e80e5005602ffbbf01c34a87f17dc88a3"},"schema_version":"1.0"},"canonical_sha256":"48b457027120098eaa923ea330ce4a7c6a16ac3bc6707f2286157f5b48018b93","source":{"kind":"arxiv","id":"1207.6321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6321","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6321v1","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6321","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"JC2FOATREAEY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JC2FOATREAEY5KUS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JC2FOATR","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JC2FOATREAEY5KUSH2RTBTSKPR","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-26T16:31:39Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"8025ff464ed9289cf399e5111ac065203291af1aa4dd6008d5bbd0d5bb9bc485","abstract_canon_sha256":"af432eea1802c005b7a7354d4fb3308e80e5005602ffbbf01c34a87f17dc88a3"},"schema_version":"1.0"},"canonical_sha256":"48b457027120098eaa923ea330ce4a7c6a16ac3bc6707f2286157f5b48018b93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:56.576834Z","signature_b64":"gzsOfqe4WcL8qJ3p/KUBnOld0DTlYa03kUZiWODvelyXN8yG1s614rRxmh7INkhnRFnT47bMoB9Fb0Dkqx3OBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48b457027120098eaa923ea330ce4a7c6a16ac3bc6707f2286157f5b48018b93","last_reissued_at":"2026-05-18T03:01:56.576198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:56.576198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6321","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":"2026-05-18T03:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAkLi+igMd/KjqQx/ABujuQWgcDGg5d0XNVNzW/73BZijb+uBGOw4YWFvBjWp2S5sscCX3WJVgh/AEsGpZ8lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:07:18.859655Z"},"content_sha256":"d00bf7b1cda4688d0df474e4a117f05f598eb824b5357d57ab72d98042b6d6aa","schema_version":"1.0","event_id":"sha256:d00bf7b1cda4688d0df474e4a117f05f598eb824b5357d57ab72d98042b6d6aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JC2FOATREAEY5KUSH2RTBTSKPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renormalization and Mellin transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"hep-th","authors_text":"Dirk Kreimer, Erik Panzer","submitted_at":"2012-07-26T16:31:39Z","abstract_excerpt":"We study renormalization in a kinetic scheme using the Hopf algebraic framework, first summarizing and recovering known results in this setting. Then we give a direct combinatorial description of renormalized amplitudes in terms of Mellin transform coefficients, featuring the universal property of rooted trees H_R. In particular, a special class of automorphisms of H_R emerges from the action of changing Mellin transforms on the Hochschild cohomology of perturbation series.\n  Furthermore, we show how the Hopf algebra of polynomials carries a refined renormalization group property, implying its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6321","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":"2026-05-18T03:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCa81o1GfSQwhZJxh76dDkozeb9LQudiCjI+fckbcrqkQmNx2S5bmIP8fJmok+7DfKt3VpQruI0UfKr4tDyEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:07:18.860265Z"},"content_sha256":"f38406d6f47a6e69301a8eb27e1c76cc4c558c5518a8b4dc0927f998810548a9","schema_version":"1.0","event_id":"sha256:f38406d6f47a6e69301a8eb27e1c76cc4c558c5518a8b4dc0927f998810548a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JC2FOATREAEY5KUSH2RTBTSKPR/bundle.json","state_url":"https://pith.science/pith/JC2FOATREAEY5KUSH2RTBTSKPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JC2FOATREAEY5KUSH2RTBTSKPR/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":"2026-05-27T07:07:18Z","links":{"resolver":"https://pith.science/pith/JC2FOATREAEY5KUSH2RTBTSKPR","bundle":"https://pith.science/pith/JC2FOATREAEY5KUSH2RTBTSKPR/bundle.json","state":"https://pith.science/pith/JC2FOATREAEY5KUSH2RTBTSKPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JC2FOATREAEY5KUSH2RTBTSKPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JC2FOATREAEY5KUSH2RTBTSKPR","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":"af432eea1802c005b7a7354d4fb3308e80e5005602ffbbf01c34a87f17dc88a3","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-26T16:31:39Z","title_canon_sha256":"8025ff464ed9289cf399e5111ac065203291af1aa4dd6008d5bbd0d5bb9bc485"},"schema_version":"1.0","source":{"id":"1207.6321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6321","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6321v1","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6321","created_at":"2026-05-18T03:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"JC2FOATREAEY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JC2FOATREAEY5KUS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JC2FOATR","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f38406d6f47a6e69301a8eb27e1c76cc4c558c5518a8b4dc0927f998810548a9","target":"graph","created_at":"2026-05-18T03:01:56Z","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":"We study renormalization in a kinetic scheme using the Hopf algebraic framework, first summarizing and recovering known results in this setting. Then we give a direct combinatorial description of renormalized amplitudes in terms of Mellin transform coefficients, featuring the universal property of rooted trees H_R. In particular, a special class of automorphisms of H_R emerges from the action of changing Mellin transforms on the Hochschild cohomology of perturbation series.\n  Furthermore, we show how the Hopf algebra of polynomials carries a refined renormalization group property, implying its","authors_text":"Dirk Kreimer, Erik Panzer","cross_cats":["math-ph","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-26T16:31:39Z","title":"Renormalization and Mellin transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6321","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:d00bf7b1cda4688d0df474e4a117f05f598eb824b5357d57ab72d98042b6d6aa","target":"record","created_at":"2026-05-18T03:01:56Z","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":"af432eea1802c005b7a7354d4fb3308e80e5005602ffbbf01c34a87f17dc88a3","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-26T16:31:39Z","title_canon_sha256":"8025ff464ed9289cf399e5111ac065203291af1aa4dd6008d5bbd0d5bb9bc485"},"schema_version":"1.0","source":{"id":"1207.6321","kind":"arxiv","version":1}},"canonical_sha256":"48b457027120098eaa923ea330ce4a7c6a16ac3bc6707f2286157f5b48018b93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48b457027120098eaa923ea330ce4a7c6a16ac3bc6707f2286157f5b48018b93","first_computed_at":"2026-05-18T03:01:56.576198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:56.576198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gzsOfqe4WcL8qJ3p/KUBnOld0DTlYa03kUZiWODvelyXN8yG1s614rRxmh7INkhnRFnT47bMoB9Fb0Dkqx3OBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:56.576834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d00bf7b1cda4688d0df474e4a117f05f598eb824b5357d57ab72d98042b6d6aa","sha256:f38406d6f47a6e69301a8eb27e1c76cc4c558c5518a8b4dc0927f998810548a9"],"state_sha256":"1f99dc6bdcae4fd60ecaa2844eb30e8ea0f2a134969e2362818ef4f173fd4faf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EzyTRb61gR7gXaU11IIXCH41mZSDPwjJNyelxS2t37HylxFI9TVI6kLH+8LTgihxP6/na3z6Upzd7KUS6oHjBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:07:18.863825Z","bundle_sha256":"781297368dd2b0a0578369c3c786621df515a2be149081e7ded5f0bdc0314b8f"}}