{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G5XTJVKLX5FUNX4XKNAZJOJD2H","short_pith_number":"pith:G5XTJVKL","canonical_record":{"source":{"id":"1312.7820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-30T18:45:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"30944e37a7ef5bcf4dcaabcd37c6e69127f7e68fff2646517bd7b916238c9740","abstract_canon_sha256":"616f2e9c2dadf329827af6b517ea55a31b04193ea94de25fd2228d659e91bbd4"},"schema_version":"1.0"},"canonical_sha256":"376f34d54bbf4b46df97534194b923d1cf214fd37c311572588e2f2c8282ee7c","source":{"kind":"arxiv","id":"1312.7820","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7820","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7820v2","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7820","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"pith_short_12","alias_value":"G5XTJVKLX5FU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G5XTJVKLX5FUNX4X","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G5XTJVKL","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G5XTJVKLX5FUNX4XKNAZJOJD2H","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-30T18:45:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"30944e37a7ef5bcf4dcaabcd37c6e69127f7e68fff2646517bd7b916238c9740","abstract_canon_sha256":"616f2e9c2dadf329827af6b517ea55a31b04193ea94de25fd2228d659e91bbd4"},"schema_version":"1.0"},"canonical_sha256":"376f34d54bbf4b46df97534194b923d1cf214fd37c311572588e2f2c8282ee7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:01.870214Z","signature_b64":"Pw+A5T+eKTMm1xgP8CXOyN2NaA/ru1eCxpFcMlttNazl6FhRY9owuzxFpV+KgipeEgaVxWDw76gnpFK9sRZCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"376f34d54bbf4b46df97534194b923d1cf214fd37c311572588e2f2c8282ee7c","last_reissued_at":"2026-05-18T02:49:01.869694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:01.869694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7820","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uh3LZptC0dybV8Bae+Og+JmO9+pfGtRxWhxMQMEZx6Uu2XsF+Oe71PJ/hGMyuWqJRnAPIN931JRCbEKPgGnWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:25:06.152344Z"},"content_sha256":"12d1032928fddce494aa018eaa38805c82cafb13989e0bf9abbe64104516c226","schema_version":"1.0","event_id":"sha256:12d1032928fddce494aa018eaa38805c82cafb13989e0bf9abbe64104516c226"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G5XTJVKLX5FUNX4XKNAZJOJD2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical connectedness of thin arithmetical discrete planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Damien Jamet, Timo Jolivet, Val\\'erie Berth\\'e, Xavier Proven\\c{c}al","submitted_at":"2013-12-30T18:45:38Z","abstract_excerpt":"An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7820","kind":"arxiv","version":2},"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":"2026-05-18T02:49:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tyeWSBFT3L2FgQWehNyFID1a2x6mrFlJ9uKhxGZzXkQ6H3rP6u92aS5EvZPRjVRp7fZ5p1GDJoIeNsNsprsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:25:06.152701Z"},"content_sha256":"a85ce3ef10ed5880e3ce34c88d228decd7ee3ab64e94ee4074e564bf4614e9f9","schema_version":"1.0","event_id":"sha256:a85ce3ef10ed5880e3ce34c88d228decd7ee3ab64e94ee4074e564bf4614e9f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/bundle.json","state_url":"https://pith.science/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/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":"2026-06-23T05:25:06Z","links":{"resolver":"https://pith.science/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H","bundle":"https://pith.science/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/bundle.json","state":"https://pith.science/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5XTJVKLX5FUNX4XKNAZJOJD2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G5XTJVKLX5FUNX4XKNAZJOJD2H","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":"616f2e9c2dadf329827af6b517ea55a31b04193ea94de25fd2228d659e91bbd4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-30T18:45:38Z","title_canon_sha256":"30944e37a7ef5bcf4dcaabcd37c6e69127f7e68fff2646517bd7b916238c9740"},"schema_version":"1.0","source":{"id":"1312.7820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7820","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7820v2","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7820","created_at":"2026-05-18T02:49:01Z"},{"alias_kind":"pith_short_12","alias_value":"G5XTJVKLX5FU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G5XTJVKLX5FUNX4X","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G5XTJVKL","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:a85ce3ef10ed5880e3ce34c88d228decd7ee3ab64e94ee4074e564bf4614e9f9","target":"graph","created_at":"2026-05-18T02:49:01Z","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":"An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version","authors_text":"Damien Jamet, Timo Jolivet, Val\\'erie Berth\\'e, Xavier Proven\\c{c}al","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-30T18:45:38Z","title":"Critical connectedness of thin arithmetical discrete planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7820","kind":"arxiv","version":2},"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":"sha256:12d1032928fddce494aa018eaa38805c82cafb13989e0bf9abbe64104516c226","target":"record","created_at":"2026-05-18T02:49:01Z","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":"616f2e9c2dadf329827af6b517ea55a31b04193ea94de25fd2228d659e91bbd4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-30T18:45:38Z","title_canon_sha256":"30944e37a7ef5bcf4dcaabcd37c6e69127f7e68fff2646517bd7b916238c9740"},"schema_version":"1.0","source":{"id":"1312.7820","kind":"arxiv","version":2}},"canonical_sha256":"376f34d54bbf4b46df97534194b923d1cf214fd37c311572588e2f2c8282ee7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"376f34d54bbf4b46df97534194b923d1cf214fd37c311572588e2f2c8282ee7c","first_computed_at":"2026-05-18T02:49:01.869694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:01.869694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pw+A5T+eKTMm1xgP8CXOyN2NaA/ru1eCxpFcMlttNazl6FhRY9owuzxFpV+KgipeEgaVxWDw76gnpFK9sRZCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:01.870214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d1032928fddce494aa018eaa38805c82cafb13989e0bf9abbe64104516c226","sha256:a85ce3ef10ed5880e3ce34c88d228decd7ee3ab64e94ee4074e564bf4614e9f9"],"state_sha256":"b47102c5887adde27eeb12dc6c6d251d638e4c719a084cb2af23748d96213b30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yt1i3lmrdqH/s2WIHaRd/JJSU0ohns4+3/IGMfgDYh3G+7NA+nxYQG4y+nyTHU4PZpHYEvWwmt7XWYQt8Y17DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:25:06.154653Z","bundle_sha256":"6788645f5d3c159a76641638fd688b9bc597ce45d84074e6a78c3a31f89ece71"}}