{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:BLZEHZTDXXUKN3RX7GOP5VETU2","short_pith_number":"pith:BLZEHZTD","canonical_record":{"source":{"id":"2010.12668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-23T21:04:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ed0506e3ad4c56e6a8d04607a90ab6d8c4fbff444ae4ee1b275b2ae008d333bd","abstract_canon_sha256":"0644b45500c37922aef402a3891415eebe6c7340fccf2666c084d83143b41128"},"schema_version":"1.0"},"canonical_sha256":"0af243e663bde8a6ee37f99cfed493a69c9f9d39603ed7134d2975c92df6d307","source":{"kind":"arxiv","id":"2010.12668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.12668","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2010.12668v1","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.12668","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"BLZEHZTDXXUK","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"BLZEHZTDXXUKN3RX","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"BLZEHZTD","created_at":"2026-07-05T01:45:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:BLZEHZTDXXUKN3RX7GOP5VETU2","target":"record","payload":{"canonical_record":{"source":{"id":"2010.12668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-23T21:04:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ed0506e3ad4c56e6a8d04607a90ab6d8c4fbff444ae4ee1b275b2ae008d333bd","abstract_canon_sha256":"0644b45500c37922aef402a3891415eebe6c7340fccf2666c084d83143b41128"},"schema_version":"1.0"},"canonical_sha256":"0af243e663bde8a6ee37f99cfed493a69c9f9d39603ed7134d2975c92df6d307","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:45:47.036278Z","signature_b64":"FaYUWI9KGitBaPRoSXuYTJTZTQUcyafbJoI6fFZ3iRo6UH2oKp9e3vxN32iezvfIhXLdUHExHYhF0P4i8ROMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0af243e663bde8a6ee37f99cfed493a69c9f9d39603ed7134d2975c92df6d307","last_reissued_at":"2026-07-05T01:45:47.035877Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:45:47.035877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.12668","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":"2026-07-05T01:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bATjjRLLN5dCmHUp4Obd91SkF3SvbZtdD9VRXx7cRlSwoj5A/vQ+PIAwZYBng85JHw2jowUDm2pA+TIFI0avBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:07:58.026400Z"},"content_sha256":"456da9a6049e9c2985e01c2c3b17471fd9280d3fdaf2da95fa041fe52b81e2e6","schema_version":"1.0","event_id":"sha256:456da9a6049e9c2985e01c2c3b17471fd9280d3fdaf2da95fa041fe52b81e2e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:BLZEHZTDXXUKN3RX7GOP5VETU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"What percent of the plane can be properly 5- and 6-colored?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Jaan Parts","submitted_at":"2020-10-23T21:04:18Z","abstract_excerpt":"We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors. It is thus shown that any unit-distance graph of order at most 6992 and 24 in the plane can be properly 6-colored and 5-colored, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.12668","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/2010.12668/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":"2026-07-05T01:45:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCWWexOIMT4XWzEGosAUdOc4j1qcolokbTIYbgTtUpFS6zVm4vGc8V9OtpUAQL6Kyh2nTkjcTyJ7LSrH6UAhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:07:58.027405Z"},"content_sha256":"ad73b1ee0fe41cf5d00cac4dca2be093a9f249eb0dda5aa32afab0c795e2e206","schema_version":"1.0","event_id":"sha256:ad73b1ee0fe41cf5d00cac4dca2be093a9f249eb0dda5aa32afab0c795e2e206"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/bundle.json","state_url":"https://pith.science/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/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":"2026-08-18T13:07:58Z","links":{"resolver":"https://pith.science/pith/BLZEHZTDXXUKN3RX7GOP5VETU2","bundle":"https://pith.science/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/bundle.json","state":"https://pith.science/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLZEHZTDXXUKN3RX7GOP5VETU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BLZEHZTDXXUKN3RX7GOP5VETU2","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":"0644b45500c37922aef402a3891415eebe6c7340fccf2666c084d83143b41128","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-23T21:04:18Z","title_canon_sha256":"ed0506e3ad4c56e6a8d04607a90ab6d8c4fbff444ae4ee1b275b2ae008d333bd"},"schema_version":"1.0","source":{"id":"2010.12668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.12668","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2010.12668v1","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.12668","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"BLZEHZTDXXUK","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"BLZEHZTDXXUKN3RX","created_at":"2026-07-05T01:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"BLZEHZTD","created_at":"2026-07-05T01:45:47Z"}],"graph_snapshots":[{"event_id":"sha256:ad73b1ee0fe41cf5d00cac4dca2be093a9f249eb0dda5aa32afab0c795e2e206","target":"graph","created_at":"2026-07-05T01:45:47Z","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/2010.12668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors. It is thus shown that any unit-distance graph of order at most 6992 and 24 in the plane can be properly 6-colored and 5-colored, respectively.","authors_text":"Jaan Parts","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-23T21:04:18Z","title":"What percent of the plane can be properly 5- and 6-colored?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.12668","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":"sha256:456da9a6049e9c2985e01c2c3b17471fd9280d3fdaf2da95fa041fe52b81e2e6","target":"record","created_at":"2026-07-05T01:45:47Z","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":"0644b45500c37922aef402a3891415eebe6c7340fccf2666c084d83143b41128","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-23T21:04:18Z","title_canon_sha256":"ed0506e3ad4c56e6a8d04607a90ab6d8c4fbff444ae4ee1b275b2ae008d333bd"},"schema_version":"1.0","source":{"id":"2010.12668","kind":"arxiv","version":1}},"canonical_sha256":"0af243e663bde8a6ee37f99cfed493a69c9f9d39603ed7134d2975c92df6d307","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0af243e663bde8a6ee37f99cfed493a69c9f9d39603ed7134d2975c92df6d307","first_computed_at":"2026-07-05T01:45:47.035877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:47.035877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FaYUWI9KGitBaPRoSXuYTJTZTQUcyafbJoI6fFZ3iRo6UH2oKp9e3vxN32iezvfIhXLdUHExHYhF0P4i8ROMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:47.036278Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.12668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:456da9a6049e9c2985e01c2c3b17471fd9280d3fdaf2da95fa041fe52b81e2e6","sha256:ad73b1ee0fe41cf5d00cac4dca2be093a9f249eb0dda5aa32afab0c795e2e206"],"state_sha256":"5d87373947b95bf443cd5b3876047bd9fb460a7fd6d387fddd607999161b27d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IE0y0x6vD15kgZ7eKGmk78DAsvELhvmj+Dob6xrY4Q6MTlpelfFz4dQqVBWdygint8SPTMeTUDtU6ctj7oYcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T13:07:58.034611Z","bundle_sha256":"67c60457c5c3100afd43ea1120aee71ebcda7a36e84aecf14709791cfcb5f8f8"}}