{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:NLCX2MR4BNXHES42D4M634QFNB","short_pith_number":"pith:NLCX2MR4","canonical_record":{"source":{"id":"2107.13460","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-07-28T16:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"45f5db3cbc69ea767c3f23a470c440dad0cee99f4d88861c913cc1de29510b42","abstract_canon_sha256":"1222971dd4d715a4c88544cd94b76c61a656f11384a31eddaca09f2ea010a1b3"},"schema_version":"1.0"},"canonical_sha256":"6ac57d323c0b6e724b9a1f19edf205687255f736f568ad9e82906439932efd26","source":{"kind":"arxiv","id":"2107.13460","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13460","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13460v3","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13460","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"NLCX2MR4BNXH","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_16","alias_value":"NLCX2MR4BNXHES42","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_8","alias_value":"NLCX2MR4","created_at":"2026-07-05T05:18:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:NLCX2MR4BNXHES42D4M634QFNB","target":"record","payload":{"canonical_record":{"source":{"id":"2107.13460","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-07-28T16:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"45f5db3cbc69ea767c3f23a470c440dad0cee99f4d88861c913cc1de29510b42","abstract_canon_sha256":"1222971dd4d715a4c88544cd94b76c61a656f11384a31eddaca09f2ea010a1b3"},"schema_version":"1.0"},"canonical_sha256":"6ac57d323c0b6e724b9a1f19edf205687255f736f568ad9e82906439932efd26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:18:59.975886Z","signature_b64":"XKPZj73loHovhEhPy5aOiwtJlKMMHIBDD112QGmR/HnEP84BvK/GLnC3f/mOixPYGfmtccQmcl6n1P7bta5hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ac57d323c0b6e724b9a1f19edf205687255f736f568ad9e82906439932efd26","last_reissued_at":"2026-07-05T05:18:59.975450Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:18:59.975450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.13460","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awEYqKg2LEF08OoVYp3kSMOVFM/0x6NDkSJHXRMp0CPS+zDyDfyhiwBDTdf9HTtQBQE590QqLSDNdR1ypGaGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:45:12.482564Z"},"content_sha256":"0b3219515eff4d6cc06e4709b02b109529168c5485c0949b1ac800297fc5af0a","schema_version":"1.0","event_id":"sha256:0b3219515eff4d6cc06e4709b02b109529168c5485c0949b1ac800297fc5af0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:NLCX2MR4BNXHES42D4M634QFNB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The number of $n$-queens configurations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Simkin","submitted_at":"2021-07-28T16:13:26Z","abstract_excerpt":"The $n$-queens problem is to determine $\\mathcal{Q}(n)$, the number of ways to place $n$ mutually non-threatening queens on an $n \\times n$ board. We show that there exists a constant $\\alpha = 1.942 \\pm 3 \\times 10^{-3}$ such that $\\mathcal{Q}(n) = ((1 \\pm o(1))ne^{-\\alpha})^n$. The constant $\\alpha$ is characterized as the solution to a convex optimization problem in $\\mathcal{P}([-1/2,1/2]^2)$, the space of Borel probability measures on the square.\n  The chief innovation is the introduction of limit objects for $n$-queens configurations, which we call queenons. These form a convex set in $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13460","kind":"arxiv","version":3},"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/2107.13460/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":"2026-07-05T05:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZQmTM/h1BFiQp7fTfpXuxhHWIiASg1JXUfErsxL6cCTMn5Em8wU9KADmLKgv3vRBnBZBkZEIlAE47ZcnKMkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:45:12.482927Z"},"content_sha256":"1cf3a9eff6dc5677db99cedbdf332f9b630b5292219b612c9d6bedb162ba0960","schema_version":"1.0","event_id":"sha256:1cf3a9eff6dc5677db99cedbdf332f9b630b5292219b612c9d6bedb162ba0960"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLCX2MR4BNXHES42D4M634QFNB/bundle.json","state_url":"https://pith.science/pith/NLCX2MR4BNXHES42D4M634QFNB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLCX2MR4BNXHES42D4M634QFNB/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":"2026-07-07T13:45:12Z","links":{"resolver":"https://pith.science/pith/NLCX2MR4BNXHES42D4M634QFNB","bundle":"https://pith.science/pith/NLCX2MR4BNXHES42D4M634QFNB/bundle.json","state":"https://pith.science/pith/NLCX2MR4BNXHES42D4M634QFNB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLCX2MR4BNXHES42D4M634QFNB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NLCX2MR4BNXHES42D4M634QFNB","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":"1222971dd4d715a4c88544cd94b76c61a656f11384a31eddaca09f2ea010a1b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-07-28T16:13:26Z","title_canon_sha256":"45f5db3cbc69ea767c3f23a470c440dad0cee99f4d88861c913cc1de29510b42"},"schema_version":"1.0","source":{"id":"2107.13460","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13460","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13460v3","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13460","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"NLCX2MR4BNXH","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_16","alias_value":"NLCX2MR4BNXHES42","created_at":"2026-07-05T05:18:59Z"},{"alias_kind":"pith_short_8","alias_value":"NLCX2MR4","created_at":"2026-07-05T05:18:59Z"}],"graph_snapshots":[{"event_id":"sha256:1cf3a9eff6dc5677db99cedbdf332f9b630b5292219b612c9d6bedb162ba0960","target":"graph","created_at":"2026-07-05T05:18:59Z","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/2107.13460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $n$-queens problem is to determine $\\mathcal{Q}(n)$, the number of ways to place $n$ mutually non-threatening queens on an $n \\times n$ board. We show that there exists a constant $\\alpha = 1.942 \\pm 3 \\times 10^{-3}$ such that $\\mathcal{Q}(n) = ((1 \\pm o(1))ne^{-\\alpha})^n$. The constant $\\alpha$ is characterized as the solution to a convex optimization problem in $\\mathcal{P}([-1/2,1/2]^2)$, the space of Borel probability measures on the square.\n  The chief innovation is the introduction of limit objects for $n$-queens configurations, which we call queenons. These form a convex set in $\\","authors_text":"Michael Simkin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-07-28T16:13:26Z","title":"The number of $n$-queens configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13460","kind":"arxiv","version":3},"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":"sha256:0b3219515eff4d6cc06e4709b02b109529168c5485c0949b1ac800297fc5af0a","target":"record","created_at":"2026-07-05T05:18:59Z","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":"1222971dd4d715a4c88544cd94b76c61a656f11384a31eddaca09f2ea010a1b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-07-28T16:13:26Z","title_canon_sha256":"45f5db3cbc69ea767c3f23a470c440dad0cee99f4d88861c913cc1de29510b42"},"schema_version":"1.0","source":{"id":"2107.13460","kind":"arxiv","version":3}},"canonical_sha256":"6ac57d323c0b6e724b9a1f19edf205687255f736f568ad9e82906439932efd26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ac57d323c0b6e724b9a1f19edf205687255f736f568ad9e82906439932efd26","first_computed_at":"2026-07-05T05:18:59.975450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:18:59.975450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKPZj73loHovhEhPy5aOiwtJlKMMHIBDD112QGmR/HnEP84BvK/GLnC3f/mOixPYGfmtccQmcl6n1P7bta5hAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:18:59.975886Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.13460","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b3219515eff4d6cc06e4709b02b109529168c5485c0949b1ac800297fc5af0a","sha256:1cf3a9eff6dc5677db99cedbdf332f9b630b5292219b612c9d6bedb162ba0960"],"state_sha256":"f77b991685917e53fe21aa7b57404cf207594555cf4948c38c45a73c824bc16c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+dixLaHK2iQocF/1pf3RaFCtbRZvz+Xj0dRrRhBm97Eel35/u3ec2oioJ8FHT0tkNM+Bt+Hf8A4lESHOkbnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:45:12.484796Z","bundle_sha256":"d6ef72d3816f3444f28961003c9b1746edfe616d964688f151ae078e35a3ba81"}}