{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7FKCTGS47QXQTFLWT2Y56AXSJE","short_pith_number":"pith:7FKCTGS4","canonical_record":{"source":{"id":"2505.00528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-01T13:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"7dba27fdd63a7519b8665f565b697f172c1473c1cf124ff68ca86d30b0e44b83","abstract_canon_sha256":"9b5a8bdda174bd64db28fb70f9dfae7e04be2909cf84c6c7b79500c1251bd1dc"},"schema_version":"1.0"},"canonical_sha256":"f954299a5cfc2f0995769eb1df02f249071d7311d1cc463e9fef1725c36fa853","source":{"kind":"arxiv","id":"2505.00528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00528","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00528v1","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00528","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"7FKCTGS47QXQ","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_16","alias_value":"7FKCTGS47QXQTFLW","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_8","alias_value":"7FKCTGS4","created_at":"2026-07-05T10:57:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7FKCTGS47QXQTFLWT2Y56AXSJE","target":"record","payload":{"canonical_record":{"source":{"id":"2505.00528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-01T13:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"7dba27fdd63a7519b8665f565b697f172c1473c1cf124ff68ca86d30b0e44b83","abstract_canon_sha256":"9b5a8bdda174bd64db28fb70f9dfae7e04be2909cf84c6c7b79500c1251bd1dc"},"schema_version":"1.0"},"canonical_sha256":"f954299a5cfc2f0995769eb1df02f249071d7311d1cc463e9fef1725c36fa853","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:14.989439Z","signature_b64":"teHBZ/LlUHEwW7fBQkwq2HEIKl/Uhua5LepLz4NEUFBINY9EjZuf/h+YC9OPQqgpoVRQr/e0vwn/oHPo+TS2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f954299a5cfc2f0995769eb1df02f249071d7311d1cc463e9fef1725c36fa853","last_reissued_at":"2026-07-05T10:57:14.988993Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:14.988993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.00528","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":"2026-07-05T10:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LGEfftWCQGyzOQ5u9j/TefAjwpGXKq4pV036+0ahhP9kta1bP8gQucHz4A0sUhjgm405VX1RWTZfE3aDFIrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:21:26.452282Z"},"content_sha256":"0941bf50c803aff90aac5d09f7649d434f14c2fbedc54593d5c8c102f1e81aa2","schema_version":"1.0","event_id":"sha256:0941bf50c803aff90aac5d09f7649d434f14c2fbedc54593d5c8c102f1e81aa2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7FKCTGS47QXQTFLWT2Y56AXSJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Analytic Zeta Function Ramp at the Black Hole Thouless Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chethan Krishnan, Pallab Basu, Suman Das","submitted_at":"2025-05-01T13:54:37Z","abstract_excerpt":"Black hole normal modes have intriguing connections to logarithmic spectra, and the spectral form factor (SFF) of $E_n = \\log n$ is the mod square of the Riemann zeta function (RZF). In this paper, we first provide an analytic understanding of the dip-ramp-plateau structure of RZF and show that the ramp at $\\beta \\equiv \\Re(s)=0$ has a slope precisely equal to 1. The $s=1$ pole of RZF can be viewed as due to a Hagedorn transition in this setting, and Riemann's analytic continuation to $\\Re(s)< 1$ provides the quantum contribution to the truncated $\\log n$ partition function. This perspective y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00528","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/2505.00528/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":"2026-07-05T10:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqHcL/YbDwBUjeeQfllvDAJ+utTXAvN5Vd3Mab8uznGvyXEW6YxhA74B1yta+Z2Lbvy/uzW1HJ/52MgocwMWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:21:26.453280Z"},"content_sha256":"762aec4db9611821e528c308a9939a6f1bbe5a61873765d351bb1f370b509c73","schema_version":"1.0","event_id":"sha256:762aec4db9611821e528c308a9939a6f1bbe5a61873765d351bb1f370b509c73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/bundle.json","state_url":"https://pith.science/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/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":"2026-08-16T13:21:26Z","links":{"resolver":"https://pith.science/pith/7FKCTGS47QXQTFLWT2Y56AXSJE","bundle":"https://pith.science/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/bundle.json","state":"https://pith.science/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FKCTGS47QXQTFLWT2Y56AXSJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7FKCTGS47QXQTFLWT2Y56AXSJE","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":"9b5a8bdda174bd64db28fb70f9dfae7e04be2909cf84c6c7b79500c1251bd1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-01T13:54:37Z","title_canon_sha256":"7dba27fdd63a7519b8665f565b697f172c1473c1cf124ff68ca86d30b0e44b83"},"schema_version":"1.0","source":{"id":"2505.00528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00528","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00528v1","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00528","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"7FKCTGS47QXQ","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_16","alias_value":"7FKCTGS47QXQTFLW","created_at":"2026-07-05T10:57:14Z"},{"alias_kind":"pith_short_8","alias_value":"7FKCTGS4","created_at":"2026-07-05T10:57:14Z"}],"graph_snapshots":[{"event_id":"sha256:762aec4db9611821e528c308a9939a6f1bbe5a61873765d351bb1f370b509c73","target":"graph","created_at":"2026-07-05T10:57:14Z","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/2505.00528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Black hole normal modes have intriguing connections to logarithmic spectra, and the spectral form factor (SFF) of $E_n = \\log n$ is the mod square of the Riemann zeta function (RZF). In this paper, we first provide an analytic understanding of the dip-ramp-plateau structure of RZF and show that the ramp at $\\beta \\equiv \\Re(s)=0$ has a slope precisely equal to 1. The $s=1$ pole of RZF can be viewed as due to a Hagedorn transition in this setting, and Riemann's analytic continuation to $\\Re(s)< 1$ provides the quantum contribution to the truncated $\\log n$ partition function. This perspective y","authors_text":"Chethan Krishnan, Pallab Basu, Suman Das","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-01T13:54:37Z","title":"An Analytic Zeta Function Ramp at the Black Hole Thouless Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00528","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":"sha256:0941bf50c803aff90aac5d09f7649d434f14c2fbedc54593d5c8c102f1e81aa2","target":"record","created_at":"2026-07-05T10:57:14Z","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":"9b5a8bdda174bd64db28fb70f9dfae7e04be2909cf84c6c7b79500c1251bd1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-01T13:54:37Z","title_canon_sha256":"7dba27fdd63a7519b8665f565b697f172c1473c1cf124ff68ca86d30b0e44b83"},"schema_version":"1.0","source":{"id":"2505.00528","kind":"arxiv","version":1}},"canonical_sha256":"f954299a5cfc2f0995769eb1df02f249071d7311d1cc463e9fef1725c36fa853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f954299a5cfc2f0995769eb1df02f249071d7311d1cc463e9fef1725c36fa853","first_computed_at":"2026-07-05T10:57:14.988993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:57:14.988993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"teHBZ/LlUHEwW7fBQkwq2HEIKl/Uhua5LepLz4NEUFBINY9EjZuf/h+YC9OPQqgpoVRQr/e0vwn/oHPo+TS2BA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:57:14.989439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0941bf50c803aff90aac5d09f7649d434f14c2fbedc54593d5c8c102f1e81aa2","sha256:762aec4db9611821e528c308a9939a6f1bbe5a61873765d351bb1f370b509c73"],"state_sha256":"a96415c2077c596ca5b5e8e814cbbf49dd11b904fef42f8562e578b1f0635fb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKG/H4OK1D+95ExG78rrpB++2fkfDFNuWm67uSr/twn8IyTgDzl2wQktOwgMfvjIIV7qMICfrwgWXMUXATllDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:21:26.459465Z","bundle_sha256":"79564d24dada5c463f4805b5cfe82c87806b4aec7c6e2cdd1c48b406529f8e5e"}}