{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BEM3ZRCZAKRNHYTFZ6352FFAWG","short_pith_number":"pith:BEM3ZRCZ","canonical_record":{"source":{"id":"2412.02068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-03T01:15:49Z","cross_cats_sorted":[],"title_canon_sha256":"54d62bb9fc8566a38f59ae5e9d2fcae7943eab8975f28e123b2475a0ba9e8e5b","abstract_canon_sha256":"55fd7db863e09d052df0dcf44e663729cea7aa4cd81d8363474f1ac6be176af4"},"schema_version":"1.0"},"canonical_sha256":"0919bcc45902a2d3e265cfb7dd14a0b182fcd3d4191a6a0a609dcdc08e0d5a41","source":{"kind":"arxiv","id":"2412.02068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.02068","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"2412.02068v1","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.02068","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"BEM3ZRCZAKRN","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_16","alias_value":"BEM3ZRCZAKRNHYTF","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_8","alias_value":"BEM3ZRCZ","created_at":"2026-07-05T09:43:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BEM3ZRCZAKRNHYTFZ6352FFAWG","target":"record","payload":{"canonical_record":{"source":{"id":"2412.02068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-03T01:15:49Z","cross_cats_sorted":[],"title_canon_sha256":"54d62bb9fc8566a38f59ae5e9d2fcae7943eab8975f28e123b2475a0ba9e8e5b","abstract_canon_sha256":"55fd7db863e09d052df0dcf44e663729cea7aa4cd81d8363474f1ac6be176af4"},"schema_version":"1.0"},"canonical_sha256":"0919bcc45902a2d3e265cfb7dd14a0b182fcd3d4191a6a0a609dcdc08e0d5a41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:43:43.513209Z","signature_b64":"MKXVYGBOy+GvZFb0CxxROdSHMRPm1b52a4yIp4rafBCVfpjG0MwPppGmSS4kaj7Gnfk5y3v66xmC0eVljzsRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0919bcc45902a2d3e265cfb7dd14a0b182fcd3d4191a6a0a609dcdc08e0d5a41","last_reissued_at":"2026-07-05T09:43:43.512796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:43:43.512796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.02068","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":"2026-07-05T09:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBJ1G5SbkDWMTb+lRQWJhxvuZZJUN5YRpd8k5iPu+UMBY7QYNsMhRKanirdCJQGx5dwg9jiuJPMK5R1rqvtUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:40:07.772743Z"},"content_sha256":"1f6402c27090f7f516d71b29e0cd590162b6add4e5eb51d4a2da6e383b931e9c","schema_version":"1.0","event_id":"sha256:1f6402c27090f7f516d71b29e0cd590162b6add4e5eb51d4a2da6e383b931e9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BEM3ZRCZAKRNHYTFZ6352FFAWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit version of Carlson's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shashi Chourasiya","submitted_at":"2024-12-03T01:15:49Z","abstract_excerpt":"Let $N(\\sigma,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $\\sigma$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson's zero density estimate, that is, $N(\\sigma, T) \\leq 0.78 T^{4 \\sigma (1- \\sigma)} (\\log T)^{5-2 \\sigma} $, with a slight improvement in the exponent of the logarithm factor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02068","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.02068/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":"2026-07-05T09:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4U3OTkENYkoRQJolLEwOgxK3kF/cLWYprK+XghUiLNpc6vjA3FSsrhCy3M/oiYRzzpgbNHVU11BqBgvkgqRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:40:07.773592Z"},"content_sha256":"f1c324d1df3f7d5cfb5b44c3a757c1244c1ea47bd21a2742cb84a7460cef679f","schema_version":"1.0","event_id":"sha256:f1c324d1df3f7d5cfb5b44c3a757c1244c1ea47bd21a2742cb84a7460cef679f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/bundle.json","state_url":"https://pith.science/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/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":"2026-08-12T15:40:07Z","links":{"resolver":"https://pith.science/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG","bundle":"https://pith.science/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/bundle.json","state":"https://pith.science/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEM3ZRCZAKRNHYTFZ6352FFAWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BEM3ZRCZAKRNHYTFZ6352FFAWG","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":"55fd7db863e09d052df0dcf44e663729cea7aa4cd81d8363474f1ac6be176af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-03T01:15:49Z","title_canon_sha256":"54d62bb9fc8566a38f59ae5e9d2fcae7943eab8975f28e123b2475a0ba9e8e5b"},"schema_version":"1.0","source":{"id":"2412.02068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.02068","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"2412.02068v1","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.02068","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"BEM3ZRCZAKRN","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_16","alias_value":"BEM3ZRCZAKRNHYTF","created_at":"2026-07-05T09:43:43Z"},{"alias_kind":"pith_short_8","alias_value":"BEM3ZRCZ","created_at":"2026-07-05T09:43:43Z"}],"graph_snapshots":[{"event_id":"sha256:f1c324d1df3f7d5cfb5b44c3a757c1244c1ea47bd21a2742cb84a7460cef679f","target":"graph","created_at":"2026-07-05T09:43:43Z","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/2412.02068/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $N(\\sigma,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $\\sigma$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson's zero density estimate, that is, $N(\\sigma, T) \\leq 0.78 T^{4 \\sigma (1- \\sigma)} (\\log T)^{5-2 \\sigma} $, with a slight improvement in the exponent of the logarithm factor.","authors_text":"Shashi Chourasiya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-03T01:15:49Z","title":"An explicit version of Carlson's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02068","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":"sha256:1f6402c27090f7f516d71b29e0cd590162b6add4e5eb51d4a2da6e383b931e9c","target":"record","created_at":"2026-07-05T09:43:43Z","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":"55fd7db863e09d052df0dcf44e663729cea7aa4cd81d8363474f1ac6be176af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-03T01:15:49Z","title_canon_sha256":"54d62bb9fc8566a38f59ae5e9d2fcae7943eab8975f28e123b2475a0ba9e8e5b"},"schema_version":"1.0","source":{"id":"2412.02068","kind":"arxiv","version":1}},"canonical_sha256":"0919bcc45902a2d3e265cfb7dd14a0b182fcd3d4191a6a0a609dcdc08e0d5a41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0919bcc45902a2d3e265cfb7dd14a0b182fcd3d4191a6a0a609dcdc08e0d5a41","first_computed_at":"2026-07-05T09:43:43.512796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:43:43.512796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MKXVYGBOy+GvZFb0CxxROdSHMRPm1b52a4yIp4rafBCVfpjG0MwPppGmSS4kaj7Gnfk5y3v66xmC0eVljzsRDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:43:43.513209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.02068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f6402c27090f7f516d71b29e0cd590162b6add4e5eb51d4a2da6e383b931e9c","sha256:f1c324d1df3f7d5cfb5b44c3a757c1244c1ea47bd21a2742cb84a7460cef679f"],"state_sha256":"a83759741aeeb182c54c19fbad1d983fbe8158a80b480f091ff1f3bacfb64634"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SbR1DkEWzG9O/+lG6aGoJ4839znow/6ngM4C40uUh9l+F9SGnuOUNEpdeZpQI9PW1D8P/BnCTUVmWrD93RIJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:40:07.789712Z","bundle_sha256":"e5f0d3421ca3c1b4a69282f617d148b7b11578d23734e9d4b194cc0973ea3153"}}