{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:B3PR5UIMZ4YBGCE3523U3JT4UW","short_pith_number":"pith:B3PR5UIM","canonical_record":{"source":{"id":"2607.16795","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T12:23:13Z","cross_cats_sorted":[],"title_canon_sha256":"8ea9cc0fd0483b10e0400a5b1444dd18be7e4d0a166422cf1882aaa969b9471c","abstract_canon_sha256":"8fd8f5beda6f3ab754373d9c801ed8996995caa5861b20bf315a28ad9c8d3e8f"},"schema_version":"1.0"},"canonical_sha256":"0edf1ed10ccf3013089beeb74da67ca59795f93955a5f31146c7157982571007","source":{"kind":"arxiv","id":"2607.16795","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16795","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16795v1","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16795","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"B3PR5UIMZ4YB","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_16","alias_value":"B3PR5UIMZ4YBGCE3","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_8","alias_value":"B3PR5UIM","created_at":"2026-07-21T01:20:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:B3PR5UIMZ4YBGCE3523U3JT4UW","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16795","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T12:23:13Z","cross_cats_sorted":[],"title_canon_sha256":"8ea9cc0fd0483b10e0400a5b1444dd18be7e4d0a166422cf1882aaa969b9471c","abstract_canon_sha256":"8fd8f5beda6f3ab754373d9c801ed8996995caa5861b20bf315a28ad9c8d3e8f"},"schema_version":"1.0"},"canonical_sha256":"0edf1ed10ccf3013089beeb74da67ca59795f93955a5f31146c7157982571007","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:20:59.362141Z","signature_b64":"30a8m4wwyNpYQ1AxFgJtMSm5DFtkDqOcY77Cz4DO/jU7KulFV3wtEKJFV7UH/mgD0Pk5gGVxckdoaoaEoH4qBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0edf1ed10ccf3013089beeb74da67ca59795f93955a5f31146c7157982571007","last_reissued_at":"2026-07-21T01:20:59.361373Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:20:59.361373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16795","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":"2026-07-21T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odeGZWdm7tFPAH0320o7lG4vLIW2ILffgVvl67zJk0yV+W5YcyhUKwYLsfnY3xjA0vU4JWmc7fNkyKrI8drMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:35:16.335948Z"},"content_sha256":"99a855aa3f379318873b2370a2feba60b4fa90ef549c7c4746fba339723ecd05","schema_version":"1.0","event_id":"sha256:99a855aa3f379318873b2370a2feba60b4fa90ef549c7c4746fba339723ecd05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:B3PR5UIMZ4YBGCE3523U3JT4UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wojciech Michalowski","submitted_at":"2026-07-18T12:23:13Z","abstract_excerpt":"Let (a_k) be the positive coefficient sequence of the normalized Riemann xi-function, and let D_{r,k} denote its consecutive Toeplitz minors. The Riemann Hypothesis is equivalent to (a_k) being a Polya frequency sequence of infinite order, and hence to nonnegativity of all Toeplitz minors. We prove that D_{r,k} > 0 for every r >= 2 and k >= 10^18 r^3. This gives an explicit cubic tail scale uniform in r, in contrast with Katkova's fixed-order asymptotic positivity. The proof does not use numerically verified zeros of the Riemann zeta-function. It combines a certified complex saddle-point analy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16795","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/2607.16795/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":"2026-07-21T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cul2ABIwW7zQdSQw5aolf2dAkosIl3c8QIfKKI2uaCIMXgmL9fuWr9e6UqctgacgXUL3j6HTaai2XM8kKziCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:35:16.336507Z"},"content_sha256":"f1a4f9c01080a0381a649e816a5943432d4feff322df0f81efddbdcf4e88eed0","schema_version":"1.0","event_id":"sha256:f1a4f9c01080a0381a649e816a5943432d4feff322df0f81efddbdcf4e88eed0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/bundle.json","state_url":"https://pith.science/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/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":"2026-08-12T03:35:16Z","links":{"resolver":"https://pith.science/pith/B3PR5UIMZ4YBGCE3523U3JT4UW","bundle":"https://pith.science/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/bundle.json","state":"https://pith.science/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3PR5UIMZ4YBGCE3523U3JT4UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B3PR5UIMZ4YBGCE3523U3JT4UW","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":"8fd8f5beda6f3ab754373d9c801ed8996995caa5861b20bf315a28ad9c8d3e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T12:23:13Z","title_canon_sha256":"8ea9cc0fd0483b10e0400a5b1444dd18be7e4d0a166422cf1882aaa969b9471c"},"schema_version":"1.0","source":{"id":"2607.16795","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16795","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16795v1","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16795","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"B3PR5UIMZ4YB","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_16","alias_value":"B3PR5UIMZ4YBGCE3","created_at":"2026-07-21T01:20:59Z"},{"alias_kind":"pith_short_8","alias_value":"B3PR5UIM","created_at":"2026-07-21T01:20:59Z"}],"graph_snapshots":[{"event_id":"sha256:f1a4f9c01080a0381a649e816a5943432d4feff322df0f81efddbdcf4e88eed0","target":"graph","created_at":"2026-07-21T01:20:59Z","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/2607.16795/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let (a_k) be the positive coefficient sequence of the normalized Riemann xi-function, and let D_{r,k} denote its consecutive Toeplitz minors. The Riemann Hypothesis is equivalent to (a_k) being a Polya frequency sequence of infinite order, and hence to nonnegativity of all Toeplitz minors. We prove that D_{r,k} > 0 for every r >= 2 and k >= 10^18 r^3. This gives an explicit cubic tail scale uniform in r, in contrast with Katkova's fixed-order asymptotic positivity. The proof does not use numerically verified zeros of the Riemann zeta-function. It combines a certified complex saddle-point analy","authors_text":"Wojciech Michalowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T12:23:13Z","title":"An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16795","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":"sha256:99a855aa3f379318873b2370a2feba60b4fa90ef549c7c4746fba339723ecd05","target":"record","created_at":"2026-07-21T01:20:59Z","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":"8fd8f5beda6f3ab754373d9c801ed8996995caa5861b20bf315a28ad9c8d3e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T12:23:13Z","title_canon_sha256":"8ea9cc0fd0483b10e0400a5b1444dd18be7e4d0a166422cf1882aaa969b9471c"},"schema_version":"1.0","source":{"id":"2607.16795","kind":"arxiv","version":1}},"canonical_sha256":"0edf1ed10ccf3013089beeb74da67ca59795f93955a5f31146c7157982571007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0edf1ed10ccf3013089beeb74da67ca59795f93955a5f31146c7157982571007","first_computed_at":"2026-07-21T01:20:59.361373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:20:59.361373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"30a8m4wwyNpYQ1AxFgJtMSm5DFtkDqOcY77Cz4DO/jU7KulFV3wtEKJFV7UH/mgD0Pk5gGVxckdoaoaEoH4qBA==","signature_status":"signed_v1","signed_at":"2026-07-21T01:20:59.362141Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16795","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a855aa3f379318873b2370a2feba60b4fa90ef549c7c4746fba339723ecd05","sha256:f1a4f9c01080a0381a649e816a5943432d4feff322df0f81efddbdcf4e88eed0"],"state_sha256":"5003f41c9592f7a6e2e5efbf7a701bb4166a034e2770c52e5fcea9c2fb5c2a47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4k+3+xhPiLD3psLkJJDQ9MnRa7vBLoiEkTgI3OfdifDz9Rb5C5DBc4rMrYzcFf2cdT/puyNTi0PzUNCUeK2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T03:35:16.340943Z","bundle_sha256":"a0dcdaff48235327bf0551976c4ba741255d55525cc6ca13307c6639c740c9d4"}}