{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5SJAXC5EC4ZWB6NVBZ3P2BKGDH","short_pith_number":"pith:5SJAXC5E","canonical_record":{"source":{"id":"2207.08555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-07-18T12:22:10Z","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"title_canon_sha256":"ba2b55d0b3d1a65867e8a5ee9f6a9214647215fe3d37d6b2324090197d8506cf","abstract_canon_sha256":"90756a4af4a8dc6f37988ac220f7f1a4a7ff665186d51250929169133cf35a90"},"schema_version":"1.0"},"canonical_sha256":"ec920b8ba4173360f9b50e76fd054619ff922ea27827aff1e692e4419bb207d5","source":{"kind":"arxiv","id":"2207.08555","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.08555","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"2207.08555v2","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.08555","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"5SJAXC5EC4ZW","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_16","alias_value":"5SJAXC5EC4ZWB6NV","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_8","alias_value":"5SJAXC5E","created_at":"2026-07-05T06:57:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5SJAXC5EC4ZWB6NVBZ3P2BKGDH","target":"record","payload":{"canonical_record":{"source":{"id":"2207.08555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-07-18T12:22:10Z","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"title_canon_sha256":"ba2b55d0b3d1a65867e8a5ee9f6a9214647215fe3d37d6b2324090197d8506cf","abstract_canon_sha256":"90756a4af4a8dc6f37988ac220f7f1a4a7ff665186d51250929169133cf35a90"},"schema_version":"1.0"},"canonical_sha256":"ec920b8ba4173360f9b50e76fd054619ff922ea27827aff1e692e4419bb207d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:57:38.164808Z","signature_b64":"95n8OIwvndloWxdWovVHO52HomNVxh1xI3XpXA6odUyEee/gPBAeqiiMynHaMObafJqZixnzLn8oZf1cUKRPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec920b8ba4173360f9b50e76fd054619ff922ea27827aff1e692e4419bb207d5","last_reissued_at":"2026-07-05T06:57:38.164310Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:57:38.164310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.08555","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":"2026-07-05T06:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+Et4jTTF8R5a1BlMyzZoNaAyNJM4ndIIPRzcflye4CBmv2U7rsg3jvmIwl1aypH7NJiD7YwUz/kfsIA9KPVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:25:29.567580Z"},"content_sha256":"915ab92d1fd3172976389537941e71802431d36ea26d5518b452b20140039d6e","schema_version":"1.0","event_id":"sha256:915ab92d1fd3172976389537941e71802431d36ea26d5518b452b20140039d6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5SJAXC5EC4ZWB6NVBZ3P2BKGDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbation theory for the $\\Phi^4_3$ measure, revisited with Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR","quant-ph"],"primary_cat":"math-ph","authors_text":"Nils Berglund, Tom Klose","submitted_at":"2022-07-18T12:22:10Z","abstract_excerpt":"We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $\\Phi^4_3$ measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We also examine the question of Borel summability of the asymptotic series. The proofs are based on Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.08555","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.08555/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0K2Z8miDlk8bOj4SBJpbx5dPPNfauLZ01Sx4LdH4l736NsDYdWillKXMXRMb4YeXSwGSjgr9MnJmVjzvpncDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:25:29.568490Z"},"content_sha256":"2a4ef5d590ea9dbacbaf1d266879985b94a5bff43c705c4dbe7f62858dd120f6","schema_version":"1.0","event_id":"sha256:2a4ef5d590ea9dbacbaf1d266879985b94a5bff43c705c4dbe7f62858dd120f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/bundle.json","state_url":"https://pith.science/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/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":"2026-08-12T04:25:29Z","links":{"resolver":"https://pith.science/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH","bundle":"https://pith.science/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/bundle.json","state":"https://pith.science/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SJAXC5EC4ZWB6NVBZ3P2BKGDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5SJAXC5EC4ZWB6NVBZ3P2BKGDH","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":"90756a4af4a8dc6f37988ac220f7f1a4a7ff665186d51250929169133cf35a90","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-07-18T12:22:10Z","title_canon_sha256":"ba2b55d0b3d1a65867e8a5ee9f6a9214647215fe3d37d6b2324090197d8506cf"},"schema_version":"1.0","source":{"id":"2207.08555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.08555","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"2207.08555v2","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.08555","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"5SJAXC5EC4ZW","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_16","alias_value":"5SJAXC5EC4ZWB6NV","created_at":"2026-07-05T06:57:38Z"},{"alias_kind":"pith_short_8","alias_value":"5SJAXC5E","created_at":"2026-07-05T06:57:38Z"}],"graph_snapshots":[{"event_id":"sha256:2a4ef5d590ea9dbacbaf1d266879985b94a5bff43c705c4dbe7f62858dd120f6","target":"graph","created_at":"2026-07-05T06:57:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.08555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $\\Phi^4_3$ measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We also examine the question of Borel summability of the asymptotic series. The proofs are based on Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation.","authors_text":"Nils Berglund, Tom Klose","cross_cats":["math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-07-18T12:22:10Z","title":"Perturbation theory for the $\\Phi^4_3$ measure, revisited with Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.08555","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":"sha256:915ab92d1fd3172976389537941e71802431d36ea26d5518b452b20140039d6e","target":"record","created_at":"2026-07-05T06:57:38Z","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":"90756a4af4a8dc6f37988ac220f7f1a4a7ff665186d51250929169133cf35a90","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-07-18T12:22:10Z","title_canon_sha256":"ba2b55d0b3d1a65867e8a5ee9f6a9214647215fe3d37d6b2324090197d8506cf"},"schema_version":"1.0","source":{"id":"2207.08555","kind":"arxiv","version":2}},"canonical_sha256":"ec920b8ba4173360f9b50e76fd054619ff922ea27827aff1e692e4419bb207d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec920b8ba4173360f9b50e76fd054619ff922ea27827aff1e692e4419bb207d5","first_computed_at":"2026-07-05T06:57:38.164310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:57:38.164310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"95n8OIwvndloWxdWovVHO52HomNVxh1xI3XpXA6odUyEee/gPBAeqiiMynHaMObafJqZixnzLn8oZf1cUKRPCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:57:38.164808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.08555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:915ab92d1fd3172976389537941e71802431d36ea26d5518b452b20140039d6e","sha256:2a4ef5d590ea9dbacbaf1d266879985b94a5bff43c705c4dbe7f62858dd120f6"],"state_sha256":"169ac49c0b22fb00fcd0b6d83c59a32f45b5fad4ff891c804b33d8171693353b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4mAH0JM3GYA7lk7+JHdGHNkqi886Ji/Qm9LhiQAXlc8juPmhITACbYLnEjybLkXyIMqrUnRuT/vDlFS+Fr+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T04:25:29.574578Z","bundle_sha256":"e82bff4e9370c15a94747ed4617b656eb81ca2911776ef1343328d2990db3293"}}