{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:RDFUBY53LBRH62BYMXYR3P3E3F","short_pith_number":"pith:RDFUBY53","canonical_record":{"source":{"id":"hep-th/0410071","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-10-07T09:59:52Z","cross_cats_sorted":["cond-mat.other","quant-ph"],"title_canon_sha256":"7df27114fd55870a161c05b6880a7ae16d1760197d342a573efddc29c63f869d","abstract_canon_sha256":"01ef2b1d7f5c1d91abec704b1fa85a5ed964ee0b38754a09079b180b66aa0711"},"schema_version":"1.0"},"canonical_sha256":"88cb40e3bb58627f683865f11dbf64d97eae01dee8fd28d0a73a2adc0a1d6663","source":{"kind":"arxiv","id":"hep-th/0410071","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0410071","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0410071v3","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0410071","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"RDFUBY53LBRH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"RDFUBY53LBRH62BY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"RDFUBY53","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:RDFUBY53LBRH62BYMXYR3P3E3F","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0410071","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-10-07T09:59:52Z","cross_cats_sorted":["cond-mat.other","quant-ph"],"title_canon_sha256":"7df27114fd55870a161c05b6880a7ae16d1760197d342a573efddc29c63f869d","abstract_canon_sha256":"01ef2b1d7f5c1d91abec704b1fa85a5ed964ee0b38754a09079b180b66aa0711"},"schema_version":"1.0"},"canonical_sha256":"88cb40e3bb58627f683865f11dbf64d97eae01dee8fd28d0a73a2adc0a1d6663","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:57.158587Z","signature_b64":"Pb9c/Fp14u2ieKkhlowQ3RqJL3rRkfs5ajx5/+y7foYoO+R/VzMdsHBLci7tvDByWsoQNKobT2v+iWevHCpyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88cb40e3bb58627f683865f11dbf64d97eae01dee8fd28d0a73a2adc0a1d6663","last_reissued_at":"2026-05-18T01:05:57.157961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:57.157961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0410071","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dOPdjsZTi/fK7bpkWwg71onQD7n2w17sJS+ol0G33FRKgaX0LtOvnqi3KOfF5b2aRAm6PB+jbddoOyruyVICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:21:28.695492Z"},"content_sha256":"316f8549e7994ecc277436290df7bba74e408402c7109b42681d7ec728956809","schema_version":"1.0","event_id":"sha256:316f8549e7994ecc277436290df7bba74e408402c7109b42681d7ec728956809"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:RDFUBY53LBRH62BYMXYR3P3E3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divergence of the $1/N_f$ series expansion in QED","license":"","headline":"","cross_cats":["cond-mat.other","quant-ph"],"primary_cat":"hep-th","authors_text":"Mofazzal Azam","submitted_at":"2004-10-07T09:59:52Z","abstract_excerpt":"The perturbative expansion series in coupling constant in QED is divergent. It is either an asymptotic series or an arrangement of a conditionally convergent series. The sum of these types of series depends on the way we arrange partial sums for successive approximations. The $1/N_f$ series expansion, where $N_f$ is the number of flavours, defines a rearrangement of this series, and therefore, its convergence would serve as a proof that the perturbative series is, in fact, conditionallyconvergent.Unfortunately, the $1/N_f$ series also diverges.We proof this usingarguments similar to those of D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0410071","kind":"arxiv","version":3},"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":"2026-05-18T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0rbJj8r5RucVhJT32J6f+GKHHDCTI7X18QtHBmx1uKBQTDLo946cyP7/R+gjpCpWfQsGztsE/ycPAm3UNPfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:21:28.695866Z"},"content_sha256":"87e93323929051a29d4da9bc30aef26e6747fed2c9d6db76ab30e94705ba8dc4","schema_version":"1.0","event_id":"sha256:87e93323929051a29d4da9bc30aef26e6747fed2c9d6db76ab30e94705ba8dc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDFUBY53LBRH62BYMXYR3P3E3F/bundle.json","state_url":"https://pith.science/pith/RDFUBY53LBRH62BYMXYR3P3E3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDFUBY53LBRH62BYMXYR3P3E3F/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":"2026-06-24T22:21:28Z","links":{"resolver":"https://pith.science/pith/RDFUBY53LBRH62BYMXYR3P3E3F","bundle":"https://pith.science/pith/RDFUBY53LBRH62BYMXYR3P3E3F/bundle.json","state":"https://pith.science/pith/RDFUBY53LBRH62BYMXYR3P3E3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDFUBY53LBRH62BYMXYR3P3E3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:RDFUBY53LBRH62BYMXYR3P3E3F","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":"01ef2b1d7f5c1d91abec704b1fa85a5ed964ee0b38754a09079b180b66aa0711","cross_cats_sorted":["cond-mat.other","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2004-10-07T09:59:52Z","title_canon_sha256":"7df27114fd55870a161c05b6880a7ae16d1760197d342a573efddc29c63f869d"},"schema_version":"1.0","source":{"id":"hep-th/0410071","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0410071","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0410071v3","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0410071","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"RDFUBY53LBRH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"RDFUBY53LBRH62BY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"RDFUBY53","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:87e93323929051a29d4da9bc30aef26e6747fed2c9d6db76ab30e94705ba8dc4","target":"graph","created_at":"2026-05-18T01:05:57Z","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":"The perturbative expansion series in coupling constant in QED is divergent. It is either an asymptotic series or an arrangement of a conditionally convergent series. The sum of these types of series depends on the way we arrange partial sums for successive approximations. The $1/N_f$ series expansion, where $N_f$ is the number of flavours, defines a rearrangement of this series, and therefore, its convergence would serve as a proof that the perturbative series is, in fact, conditionallyconvergent.Unfortunately, the $1/N_f$ series also diverges.We proof this usingarguments similar to those of D","authors_text":"Mofazzal Azam","cross_cats":["cond-mat.other","quant-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-10-07T09:59:52Z","title":"Divergence of the $1/N_f$ series expansion in QED"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0410071","kind":"arxiv","version":3},"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":"sha256:316f8549e7994ecc277436290df7bba74e408402c7109b42681d7ec728956809","target":"record","created_at":"2026-05-18T01:05:57Z","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":"01ef2b1d7f5c1d91abec704b1fa85a5ed964ee0b38754a09079b180b66aa0711","cross_cats_sorted":["cond-mat.other","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2004-10-07T09:59:52Z","title_canon_sha256":"7df27114fd55870a161c05b6880a7ae16d1760197d342a573efddc29c63f869d"},"schema_version":"1.0","source":{"id":"hep-th/0410071","kind":"arxiv","version":3}},"canonical_sha256":"88cb40e3bb58627f683865f11dbf64d97eae01dee8fd28d0a73a2adc0a1d6663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88cb40e3bb58627f683865f11dbf64d97eae01dee8fd28d0a73a2adc0a1d6663","first_computed_at":"2026-05-18T01:05:57.157961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:57.157961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pb9c/Fp14u2ieKkhlowQ3RqJL3rRkfs5ajx5/+y7foYoO+R/VzMdsHBLci7tvDByWsoQNKobT2v+iWevHCpyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:57.158587Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0410071","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:316f8549e7994ecc277436290df7bba74e408402c7109b42681d7ec728956809","sha256:87e93323929051a29d4da9bc30aef26e6747fed2c9d6db76ab30e94705ba8dc4"],"state_sha256":"7541d8f5b3cd0a4135838bca93f3cad7ce10f995787d657cb161bd86cc680e25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dfI4l4At1cp1UvofrlYGjMj3penhKJaKzeEzT168k974NmP7T1ppsRaJENIsht6O2iT9lp931ZB2kVLq10Z0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:21:28.699013Z","bundle_sha256":"26a1ec7f28a3afc24b9cff96a192c85240871fd7bcfb259c0c964760e796ca1b"}}