{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ERYXN4W232GO7FG3NWVLR7EQQ6","short_pith_number":"pith:ERYXN4W2","canonical_record":{"source":{"id":"1602.04637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8635f19256bd622894a624bc450f00562d1661925fdd0c6ccb837fdb81b5b48b","abstract_canon_sha256":"2f05d68e16da2fa61929b0f45043978144c08758491b1935b50e3246ce3e6b6a"},"schema_version":"1.0"},"canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","source":{"kind":"arxiv","id":"1602.04637","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04637","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04637v2","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04637","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"pith_short_12","alias_value":"ERYXN4W232GO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ERYXN4W232GO7FG3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ERYXN4W2","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ERYXN4W232GO7FG3NWVLR7EQQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8635f19256bd622894a624bc450f00562d1661925fdd0c6ccb837fdb81b5b48b","abstract_canon_sha256":"2f05d68e16da2fa61929b0f45043978144c08758491b1935b50e3246ce3e6b6a"},"schema_version":"1.0"},"canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.253650Z","signature_b64":"yLfouh+JKPNMf7JBj4D/dCOjvkn6bAQcPQuwRzaMX8/vy8knpLAGgR2ACcQfnrB3H6SrenV1/UGPAbr/+ey/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","last_reissued_at":"2026-05-18T00:31:56.253171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.253171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04637","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":"2026-05-18T00:31:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HdxL2EfdBdEP9D6JEAJTT+qb23YqEk8Kxct8Ndj0xloTwLEQt1/mTkwVcbzWp+FnRXqai68zhaX4OtPWdaPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:59:59.302678Z"},"content_sha256":"082bc0aa598cfed359e635c5a7b357e6253ed8b0279ea0373bb1f93b2c0ddc45","schema_version":"1.0","event_id":"sha256:082bc0aa598cfed359e635c5a7b357e6253ed8b0279ea0373bb1f93b2c0ddc45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ERYXN4W232GO7FG3NWVLR7EQQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incircular nets and confocal conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Alexander I. Bobenko, Arseniy Akopyan","submitted_at":"2016-02-15T11:36:40Z","abstract_excerpt":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics.\n  Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite natur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04637","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":"2026-05-18T00:31:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SK+QL0Aj4mtZrEa5ovXLCpnucyecZj/8pjIShIc3Hrnpp8jPeL/c7i9MjqAqaCzK62cU0pdMb8dAMigvt4gBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:59:59.303023Z"},"content_sha256":"8f6a48f654e6d1ded204e3af340afb7201e679bf981a659d8b11a2048b27bb1d","schema_version":"1.0","event_id":"sha256:8f6a48f654e6d1ded204e3af340afb7201e679bf981a659d8b11a2048b27bb1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/bundle.json","state_url":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/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":"2026-05-28T12:59:59Z","links":{"resolver":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6","bundle":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/bundle.json","state":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ERYXN4W232GO7FG3NWVLR7EQQ6","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":"2f05d68e16da2fa61929b0f45043978144c08758491b1935b50e3246ce3e6b6a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","title_canon_sha256":"8635f19256bd622894a624bc450f00562d1661925fdd0c6ccb837fdb81b5b48b"},"schema_version":"1.0","source":{"id":"1602.04637","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04637","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04637v2","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04637","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"pith_short_12","alias_value":"ERYXN4W232GO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ERYXN4W232GO7FG3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ERYXN4W2","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:8f6a48f654e6d1ded204e3af340afb7201e679bf981a659d8b11a2048b27bb1d","target":"graph","created_at":"2026-05-18T00:31:56Z","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 consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics.\n  Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite natur","authors_text":"Alexander I. Bobenko, Arseniy Akopyan","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","title":"Incircular nets and confocal conics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04637","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":"sha256:082bc0aa598cfed359e635c5a7b357e6253ed8b0279ea0373bb1f93b2c0ddc45","target":"record","created_at":"2026-05-18T00:31:56Z","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":"2f05d68e16da2fa61929b0f45043978144c08758491b1935b50e3246ce3e6b6a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","title_canon_sha256":"8635f19256bd622894a624bc450f00562d1661925fdd0c6ccb837fdb81b5b48b"},"schema_version":"1.0","source":{"id":"1602.04637","kind":"arxiv","version":2}},"canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","first_computed_at":"2026-05-18T00:31:56.253171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:56.253171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yLfouh+JKPNMf7JBj4D/dCOjvkn6bAQcPQuwRzaMX8/vy8knpLAGgR2ACcQfnrB3H6SrenV1/UGPAbr/+ey/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:56.253650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04637","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:082bc0aa598cfed359e635c5a7b357e6253ed8b0279ea0373bb1f93b2c0ddc45","sha256:8f6a48f654e6d1ded204e3af340afb7201e679bf981a659d8b11a2048b27bb1d"],"state_sha256":"bc520fcf4cbbbf943f07defb2e8a8ecae7bdfd00f9335404db0dbe8e0ed92c64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNyQyBU8rwjP4KX+7H0oYMesdqhRxMbltyQdZNcOBOMPiPlmK1CuME7nzDSnUqHwdsvdChzgcYwoD08rGABgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:59:59.305100Z","bundle_sha256":"0656c1b7f646f63ba3aead97513f1b124eb37e09ae86be5a2afb6f3704317ea8"}}