{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DICJI56XT5HKVOAV2RS5VRGOBR","short_pith_number":"pith:DICJI56X","canonical_record":{"source":{"id":"1203.4295","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2012-03-20T00:18:50Z","cross_cats_sorted":[],"title_canon_sha256":"eb6acafa2dad3c7cb5a2a60235f0126ae2ebade2d3c31d1a64e5add9b7ba616c","abstract_canon_sha256":"be0baa5b1851e7012b74f1bbc0242b1b9025035305635271de89b9c0072461e0"},"schema_version":"1.0"},"canonical_sha256":"1a049477d79f4eaab815d465dac4ce0c5d9e535a20df1a374e5f1058cf2e0ff6","source":{"kind":"arxiv","id":"1203.4295","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4295","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4295v3","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4295","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"DICJI56XT5HK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DICJI56XT5HKVOAV","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DICJI56X","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DICJI56XT5HKVOAV2RS5VRGOBR","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4295","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2012-03-20T00:18:50Z","cross_cats_sorted":[],"title_canon_sha256":"eb6acafa2dad3c7cb5a2a60235f0126ae2ebade2d3c31d1a64e5add9b7ba616c","abstract_canon_sha256":"be0baa5b1851e7012b74f1bbc0242b1b9025035305635271de89b9c0072461e0"},"schema_version":"1.0"},"canonical_sha256":"1a049477d79f4eaab815d465dac4ce0c5d9e535a20df1a374e5f1058cf2e0ff6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:21.884901Z","signature_b64":"lZY9cXIXbPXipE4JuV28IQ94epfCZan92piS0rHD41yLqMpCSJw2GTpdYgb4JdK+6iUDEf5Ul2/47xGfxEUoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a049477d79f4eaab815d465dac4ce0c5d9e535a20df1a374e5f1058cf2e0ff6","last_reissued_at":"2026-05-18T03:56:21.884195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:21.884195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4295","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":"2026-05-18T03:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABMTOFkfg77CRJ2g+dL3EiUymw2HNGHdLJfL4W6j0n9s96rzCZ2W88fgagevz6z81y2bHqMXl1Ss9zwlOJUMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:36:20.641457Z"},"content_sha256":"5166731ff3e453c61228ca3aa4f945e58319443b5926db8713c6fa531dca22a5","schema_version":"1.0","event_id":"sha256:5166731ff3e453c61228ca3aa4f945e58319443b5926db8713c6fa531dca22a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DICJI56XT5HKVOAV2RS5VRGOBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Inhomogeneous Hall's Ray","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. D. Pollington, D. J. Crisp, W. Moran","submitted_at":"2012-03-20T00:18:50Z","abstract_excerpt":"We show that the inhomogenous approximation spectrum, associated to an irrational number \\alpha\\ always has a Hall's Ray; that is, there is an \\epsilon>0 such that [0,\\epsilon) is a subset of the spectrum. In the case when \\alpha\\ has unbounded partial quotients we show that the spectrum is just a ray."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4295","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":""},"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":"2026-05-18T03:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrP7j2c79po2dqAb8qFFO+SRK7BEFxylF/5Z6OOesRyulbjM+V9wQvH486ERVdEjhlKEeV9m4UDwqafzSdnPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:36:20.641788Z"},"content_sha256":"8006f2fa7642a245c06173e663b5256d1e55c1a6955cb32e3d9764749f2b5768","schema_version":"1.0","event_id":"sha256:8006f2fa7642a245c06173e663b5256d1e55c1a6955cb32e3d9764749f2b5768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DICJI56XT5HKVOAV2RS5VRGOBR/bundle.json","state_url":"https://pith.science/pith/DICJI56XT5HKVOAV2RS5VRGOBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DICJI56XT5HKVOAV2RS5VRGOBR/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":"2026-07-07T12:36:20Z","links":{"resolver":"https://pith.science/pith/DICJI56XT5HKVOAV2RS5VRGOBR","bundle":"https://pith.science/pith/DICJI56XT5HKVOAV2RS5VRGOBR/bundle.json","state":"https://pith.science/pith/DICJI56XT5HKVOAV2RS5VRGOBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DICJI56XT5HKVOAV2RS5VRGOBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DICJI56XT5HKVOAV2RS5VRGOBR","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":"be0baa5b1851e7012b74f1bbc0242b1b9025035305635271de89b9c0072461e0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2012-03-20T00:18:50Z","title_canon_sha256":"eb6acafa2dad3c7cb5a2a60235f0126ae2ebade2d3c31d1a64e5add9b7ba616c"},"schema_version":"1.0","source":{"id":"1203.4295","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4295","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4295v3","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4295","created_at":"2026-05-18T03:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"DICJI56XT5HK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DICJI56XT5HKVOAV","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DICJI56X","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:8006f2fa7642a245c06173e663b5256d1e55c1a6955cb32e3d9764749f2b5768","target":"graph","created_at":"2026-05-18T03:56:21Z","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":"We show that the inhomogenous approximation spectrum, associated to an irrational number \\alpha\\ always has a Hall's Ray; that is, there is an \\epsilon>0 such that [0,\\epsilon) is a subset of the spectrum. In the case when \\alpha\\ has unbounded partial quotients we show that the spectrum is just a ray.","authors_text":"A. D. Pollington, D. J. Crisp, W. Moran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2012-03-20T00:18:50Z","title":"The Inhomogeneous Hall's Ray"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4295","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":"sha256:5166731ff3e453c61228ca3aa4f945e58319443b5926db8713c6fa531dca22a5","target":"record","created_at":"2026-05-18T03:56:21Z","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":"be0baa5b1851e7012b74f1bbc0242b1b9025035305635271de89b9c0072461e0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2012-03-20T00:18:50Z","title_canon_sha256":"eb6acafa2dad3c7cb5a2a60235f0126ae2ebade2d3c31d1a64e5add9b7ba616c"},"schema_version":"1.0","source":{"id":"1203.4295","kind":"arxiv","version":3}},"canonical_sha256":"1a049477d79f4eaab815d465dac4ce0c5d9e535a20df1a374e5f1058cf2e0ff6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a049477d79f4eaab815d465dac4ce0c5d9e535a20df1a374e5f1058cf2e0ff6","first_computed_at":"2026-05-18T03:56:21.884195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:21.884195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lZY9cXIXbPXipE4JuV28IQ94epfCZan92piS0rHD41yLqMpCSJw2GTpdYgb4JdK+6iUDEf5Ul2/47xGfxEUoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:21.884901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4295","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5166731ff3e453c61228ca3aa4f945e58319443b5926db8713c6fa531dca22a5","sha256:8006f2fa7642a245c06173e663b5256d1e55c1a6955cb32e3d9764749f2b5768"],"state_sha256":"6dc88ff62350e5e29fef13844eb000e574506970a67957a55d792219ea3a4036"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eAU3+IaxtBZx1c5ew5REm06cBFr27bMCkEGYHK+2bxMYPh8OxIx/ePapDPW9vk6fDy4u5hee+2fhhNseYyD2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:36:20.643651Z","bundle_sha256":"12511f74e4debd92a4c31778fa6edfc2c31ba3799b54d2fa5b80c187b4275eea"}}