{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:H4KSVNCABXPLKGZFVT65FBGMFG","short_pith_number":"pith:H4KSVNCA","canonical_record":{"source":{"id":"1107.2809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-14T13:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"15a281b8af9baa7e180599675ddb9f26979903efa86a62b72ea2bb3fbe16ca98","abstract_canon_sha256":"fde88963231d6c71ff90f9499f1b72ccf1db0438cad52bbc5ea673e2b8db0c8c"},"schema_version":"1.0"},"canonical_sha256":"3f152ab4400ddeb51b25acfdd284cc29886b48fb9ead1c4e9d4844157149ab87","source":{"kind":"arxiv","id":"1107.2809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2809","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2809v1","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2809","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"H4KSVNCABXPL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H4KSVNCABXPLKGZF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H4KSVNCA","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:H4KSVNCABXPLKGZFVT65FBGMFG","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-14T13:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"15a281b8af9baa7e180599675ddb9f26979903efa86a62b72ea2bb3fbe16ca98","abstract_canon_sha256":"fde88963231d6c71ff90f9499f1b72ccf1db0438cad52bbc5ea673e2b8db0c8c"},"schema_version":"1.0"},"canonical_sha256":"3f152ab4400ddeb51b25acfdd284cc29886b48fb9ead1c4e9d4844157149ab87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:42.076054Z","signature_b64":"KXvB+VCKt+6eQ9fDRazt8nGBpnyz1Eoxz+paGFRdG8QjDr8oRnSKUOjmMtRLSGfJ7FoFxNrNEHjqZqau7b22Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f152ab4400ddeb51b25acfdd284cc29886b48fb9ead1c4e9d4844157149ab87","last_reissued_at":"2026-05-18T04:04:42.075492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:42.075492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2809","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":"2026-05-18T04:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c6KQZmPtO5vG2r4OQ2174McXvUqBFvLUmMXC3UPN5GV+GSG9E7xS02INW/BuL/E0bIdu5cBuOWrJWOuB+39FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:36:32.267428Z"},"content_sha256":"92a72098bd06c0843b274bea0542d89be907285364cf2b5a084ab884fb956fae","schema_version":"1.0","event_id":"sha256:92a72098bd06c0843b274bea0542d89be907285364cf2b5a084ab884fb956fae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:H4KSVNCABXPLKGZFVT65FBGMFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Skewes number for twin primes: counting sign changes of $\\pi_2(x)-C_2 \\Li_2(x)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marek Wolf","submitted_at":"2011-07-14T13:02:53Z","abstract_excerpt":"The results of the computer investigation of the sign changes of the difference between the number of twin primes $\\pi_2(x)$ and the Hardy--Littlewood conjecture $C_2\\Li_2(x)$ are reported. It turns out that $d_2(x)=\\pi_2(x) - C_2\\Li_2(x)$ changes the sign at unexpectedly low values of $x$ and for $x<2^{48}=2.81\\...\\times10^{14}$ there are 477118 sign changes of this difference. It is conjectured that the number of sign changes of $d_2(x)$ for $x\\in (1, T)$ is given by $\\sqrt T/\\log(T)$. The running logarithmic densities of the sets for which $d_2(x)>0$ and $d_2(x)<0$ are plotted for $x$ up to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2809","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":""},"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":"2026-05-18T04:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGjkfgHTv6BYR+xODEPLNy2u/OnWUBEPm7eOZAl6CfnnB/5gH+jd3gGD56GMVlztqftdrvxLM14OCDHg44rwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:36:32.267806Z"},"content_sha256":"ef238b31853d01b5305774b86cc5ccae9afb668636c9baece877741b19b0543d","schema_version":"1.0","event_id":"sha256:ef238b31853d01b5305774b86cc5ccae9afb668636c9baece877741b19b0543d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4KSVNCABXPLKGZFVT65FBGMFG/bundle.json","state_url":"https://pith.science/pith/H4KSVNCABXPLKGZFVT65FBGMFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4KSVNCABXPLKGZFVT65FBGMFG/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":"2026-05-30T07:36:32Z","links":{"resolver":"https://pith.science/pith/H4KSVNCABXPLKGZFVT65FBGMFG","bundle":"https://pith.science/pith/H4KSVNCABXPLKGZFVT65FBGMFG/bundle.json","state":"https://pith.science/pith/H4KSVNCABXPLKGZFVT65FBGMFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4KSVNCABXPLKGZFVT65FBGMFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H4KSVNCABXPLKGZFVT65FBGMFG","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":"fde88963231d6c71ff90f9499f1b72ccf1db0438cad52bbc5ea673e2b8db0c8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-14T13:02:53Z","title_canon_sha256":"15a281b8af9baa7e180599675ddb9f26979903efa86a62b72ea2bb3fbe16ca98"},"schema_version":"1.0","source":{"id":"1107.2809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2809","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2809v1","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2809","created_at":"2026-05-18T04:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"H4KSVNCABXPL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H4KSVNCABXPLKGZF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H4KSVNCA","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:ef238b31853d01b5305774b86cc5ccae9afb668636c9baece877741b19b0543d","target":"graph","created_at":"2026-05-18T04:04:42Z","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 results of the computer investigation of the sign changes of the difference between the number of twin primes $\\pi_2(x)$ and the Hardy--Littlewood conjecture $C_2\\Li_2(x)$ are reported. It turns out that $d_2(x)=\\pi_2(x) - C_2\\Li_2(x)$ changes the sign at unexpectedly low values of $x$ and for $x<2^{48}=2.81\\...\\times10^{14}$ there are 477118 sign changes of this difference. It is conjectured that the number of sign changes of $d_2(x)$ for $x\\in (1, T)$ is given by $\\sqrt T/\\log(T)$. The running logarithmic densities of the sets for which $d_2(x)>0$ and $d_2(x)<0$ are plotted for $x$ up to","authors_text":"Marek Wolf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-14T13:02:53Z","title":"The Skewes number for twin primes: counting sign changes of $\\pi_2(x)-C_2 \\Li_2(x)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2809","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":"sha256:92a72098bd06c0843b274bea0542d89be907285364cf2b5a084ab884fb956fae","target":"record","created_at":"2026-05-18T04:04:42Z","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":"fde88963231d6c71ff90f9499f1b72ccf1db0438cad52bbc5ea673e2b8db0c8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-14T13:02:53Z","title_canon_sha256":"15a281b8af9baa7e180599675ddb9f26979903efa86a62b72ea2bb3fbe16ca98"},"schema_version":"1.0","source":{"id":"1107.2809","kind":"arxiv","version":1}},"canonical_sha256":"3f152ab4400ddeb51b25acfdd284cc29886b48fb9ead1c4e9d4844157149ab87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f152ab4400ddeb51b25acfdd284cc29886b48fb9ead1c4e9d4844157149ab87","first_computed_at":"2026-05-18T04:04:42.075492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:42.075492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KXvB+VCKt+6eQ9fDRazt8nGBpnyz1Eoxz+paGFRdG8QjDr8oRnSKUOjmMtRLSGfJ7FoFxNrNEHjqZqau7b22Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:42.076054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a72098bd06c0843b274bea0542d89be907285364cf2b5a084ab884fb956fae","sha256:ef238b31853d01b5305774b86cc5ccae9afb668636c9baece877741b19b0543d"],"state_sha256":"d2bd6367c0c23f6b7ebac9725a4cfed009a54f13408e2f243d07b4934f1a323a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDdyGmLf1JKCBC9Gr2RCMYnWiLl6Hbq5Q8VZVIrlrHY/wzbEjC6RGZ9jay+zSEfMN/urEH1eYHUv4zfRPvmaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:36:32.270033Z","bundle_sha256":"7335c7deaf2811ad1d6717b02b590cc4db607ec901c71a0c582eb495c8883097"}}