{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J7DRGGWLJQUJN3MRMULK24AC5S","short_pith_number":"pith:J7DRGGWL","canonical_record":{"source":{"id":"2507.15334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-21T07:47:54Z","cross_cats_sorted":[],"title_canon_sha256":"b273b1883a136015682a35e7956df61f79ab11e8f8faa54385eec68583fc7152","abstract_canon_sha256":"469e950ab35a2a419c01842ff2151efd1a6643810d40cb927523f02d7ea8f567"},"schema_version":"1.0"},"canonical_sha256":"4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8","source":{"kind":"arxiv","id":"2507.15334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15334","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15334v2","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15334","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"J7DRGGWLJQUJ","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"J7DRGGWLJQUJN3MR","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"J7DRGGWL","created_at":"2026-05-20T01:04:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J7DRGGWLJQUJN3MRMULK24AC5S","target":"record","payload":{"canonical_record":{"source":{"id":"2507.15334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-21T07:47:54Z","cross_cats_sorted":[],"title_canon_sha256":"b273b1883a136015682a35e7956df61f79ab11e8f8faa54385eec68583fc7152","abstract_canon_sha256":"469e950ab35a2a419c01842ff2151efd1a6643810d40cb927523f02d7ea8f567"},"schema_version":"1.0"},"canonical_sha256":"4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:04:56.191265Z","signature_b64":"WmVfq+wRpEJcwhSJiRe67q731BAOSXpH0H4KMEMOXXY4OaYIrpOhsUHsjdJvh03dkojP2BJVlJLhTWREvjfkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8","last_reissued_at":"2026-05-20T01:04:56.190279Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:04:56.190279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.15334","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":"2026-05-20T01:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0860oXQMZNfla7F3CsySG13cCvRrWwNWICxy2VXnmjVidtjib+nhOoRsKf5xmHRBnFYOv7Sea1xVsO7nKMcJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:00:25.733185Z"},"content_sha256":"bc65ac48c0cf563a6f31247dfb3bef5373443c33d8ea3bfc8b6abd5366745186","schema_version":"1.0","event_id":"sha256:bc65ac48c0cf563a6f31247dfb3bef5373443c33d8ea3bfc8b6abd5366745186"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J7DRGGWLJQUJN3MRMULK24AC5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refinements for primes in short arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Harm","submitted_at":"2025-07-21T07:47:54Z","abstract_excerpt":"Given a zero-free region and an averaged zero-density estimate over all Dirichlet $L$-functions modulo $q\\in\\mathbb{N}$, we refine the error terms of the prime number theorem in all and almost all short arithmetic progressions. For example, if we assume the Generalized Density Hypothesis, then for any arithmetic progression modulo $q\\leq \\log^{\\ell} x$ with $\\ell>0$ and any $\\varepsilon>0$, the prime number theorem holds in all intervals $(x-\\sqrt{x}\\exp(\\log^{\\frac{2}{3}+\\varepsilon} x),x]$ and almost all intervals $(x-\\exp(\\log^{\\frac{2}{3}+\\varepsilon} x),x]$ as $x\\rightarrow\\infty$. This r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15334","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/2507.15334/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":"2026-05-20T01:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U283rbdtg85xfF7l/lLXvurm0OBoAtqgGCTIDhGYNmQ0o0md5DZvOnvZ6/kaoIdwNwCDilCNyhVmljGAt/OTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:00:25.733870Z"},"content_sha256":"b17f43e7ec0e68b6a882cf1a7b535286d5804cae87949e3358ac3477c243b57b","schema_version":"1.0","event_id":"sha256:b17f43e7ec0e68b6a882cf1a7b535286d5804cae87949e3358ac3477c243b57b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7DRGGWLJQUJN3MRMULK24AC5S/bundle.json","state_url":"https://pith.science/pith/J7DRGGWLJQUJN3MRMULK24AC5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7DRGGWLJQUJN3MRMULK24AC5S/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":"2026-05-27T06:00:25Z","links":{"resolver":"https://pith.science/pith/J7DRGGWLJQUJN3MRMULK24AC5S","bundle":"https://pith.science/pith/J7DRGGWLJQUJN3MRMULK24AC5S/bundle.json","state":"https://pith.science/pith/J7DRGGWLJQUJN3MRMULK24AC5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7DRGGWLJQUJN3MRMULK24AC5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J7DRGGWLJQUJN3MRMULK24AC5S","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":"469e950ab35a2a419c01842ff2151efd1a6643810d40cb927523f02d7ea8f567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-21T07:47:54Z","title_canon_sha256":"b273b1883a136015682a35e7956df61f79ab11e8f8faa54385eec68583fc7152"},"schema_version":"1.0","source":{"id":"2507.15334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15334","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15334v2","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15334","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"J7DRGGWLJQUJ","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"J7DRGGWLJQUJN3MR","created_at":"2026-05-20T01:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"J7DRGGWL","created_at":"2026-05-20T01:04:56Z"}],"graph_snapshots":[{"event_id":"sha256:b17f43e7ec0e68b6a882cf1a7b535286d5804cae87949e3358ac3477c243b57b","target":"graph","created_at":"2026-05-20T01:04:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.15334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a zero-free region and an averaged zero-density estimate over all Dirichlet $L$-functions modulo $q\\in\\mathbb{N}$, we refine the error terms of the prime number theorem in all and almost all short arithmetic progressions. For example, if we assume the Generalized Density Hypothesis, then for any arithmetic progression modulo $q\\leq \\log^{\\ell} x$ with $\\ell>0$ and any $\\varepsilon>0$, the prime number theorem holds in all intervals $(x-\\sqrt{x}\\exp(\\log^{\\frac{2}{3}+\\varepsilon} x),x]$ and almost all intervals $(x-\\exp(\\log^{\\frac{2}{3}+\\varepsilon} x),x]$ as $x\\rightarrow\\infty$. This r","authors_text":"Michael Harm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-21T07:47:54Z","title":"Refinements for primes in short arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15334","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:bc65ac48c0cf563a6f31247dfb3bef5373443c33d8ea3bfc8b6abd5366745186","target":"record","created_at":"2026-05-20T01:04:56Z","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":"469e950ab35a2a419c01842ff2151efd1a6643810d40cb927523f02d7ea8f567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-21T07:47:54Z","title_canon_sha256":"b273b1883a136015682a35e7956df61f79ab11e8f8faa54385eec68583fc7152"},"schema_version":"1.0","source":{"id":"2507.15334","kind":"arxiv","version":2}},"canonical_sha256":"4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8","first_computed_at":"2026-05-20T01:04:56.190279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:04:56.190279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WmVfq+wRpEJcwhSJiRe67q731BAOSXpH0H4KMEMOXXY4OaYIrpOhsUHsjdJvh03dkojP2BJVlJLhTWREvjfkDA==","signature_status":"signed_v1","signed_at":"2026-05-20T01:04:56.191265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.15334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc65ac48c0cf563a6f31247dfb3bef5373443c33d8ea3bfc8b6abd5366745186","sha256:b17f43e7ec0e68b6a882cf1a7b535286d5804cae87949e3358ac3477c243b57b"],"state_sha256":"8e44f53ca56f1983691ece01ef01a950c3b323d999042d4b26ca87d63d89b6a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TUcNsaR+TFunLB1rFbp5IwQNhR78CpIUi7lYmQ20iaCLUwOaJYe3+dsDGrdwETYB31qiaAxKg6sCSSAmw7yQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:00:25.737553Z","bundle_sha256":"7f44473ae3d4f0121494fbf7b10e47ba124e59dd9265c1c47baf3f34a16bb35e"}}