{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3Q4UIOR2VELXNTQIUXKN25IXXY","short_pith_number":"pith:3Q4UIOR2","canonical_record":{"source":{"id":"2607.29236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-31T10:12:24Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"20a6f8711d3b363cb93db1e06b36ecf5262d7a3f9e0a1fb0cbec282afea8e2f1","abstract_canon_sha256":"29a2c82fb3a595ecec528cf408b5554d2993a34eebf7fcecdfe88957dd5de2a7"},"schema_version":"1.0"},"canonical_sha256":"dc39443a3aa91776ce08a5d4dd7517be0241a6ae96cb107c1d86a9f242a4c6a0","source":{"kind":"arxiv","id":"2607.29236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29236","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29236v1","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29236","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"3Q4UIOR2VELX","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_16","alias_value":"3Q4UIOR2VELXNTQI","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_8","alias_value":"3Q4UIOR2","created_at":"2026-08-03T01:22:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3Q4UIOR2VELXNTQIUXKN25IXXY","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-31T10:12:24Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"20a6f8711d3b363cb93db1e06b36ecf5262d7a3f9e0a1fb0cbec282afea8e2f1","abstract_canon_sha256":"29a2c82fb3a595ecec528cf408b5554d2993a34eebf7fcecdfe88957dd5de2a7"},"schema_version":"1.0"},"canonical_sha256":"dc39443a3aa91776ce08a5d4dd7517be0241a6ae96cb107c1d86a9f242a4c6a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:22:25.320086Z","signature_b64":"NTZmA1PP/yrOlv25l0ujH/F+hTUN7YJCVr7kLYMHTcqvqopbz3SZ9+L9Kms3yI70SVo4+8/darcKODrqQqMyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc39443a3aa91776ce08a5d4dd7517be0241a6ae96cb107c1d86a9f242a4c6a0","last_reissued_at":"2026-08-03T01:22:25.318449Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:22:25.318449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29236","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":"2026-08-03T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFvUcGDCNB3+kM2m3SwUU9QzFcZrIDdhhRpSoM9MtprzmMNPYXoz/u7zHDJ8pDcy/aS7JaMAjCO/EquyO/PrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:41:36.277610Z"},"content_sha256":"b6efeee9994086e0ddac4c65557f43af9fc12190e42f6bf90a39e9a7a152be75","schema_version":"1.0","event_id":"sha256:b6efeee9994086e0ddac4c65557f43af9fc12190e42f6bf90a39e9a7a152be75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3Q4UIOR2VELXNTQIUXKN25IXXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration and Classification of Triangle-Maximal Pseudoline Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Denis Utkin, Roman Parpalak","submitted_at":"2026-07-31T10:12:24Z","abstract_excerpt":"We describe algorithms for the exhaustive enumeration and classification of simple arrangements of $n$ pseudolines ($n$ odd) maximizing the number of triangular faces. The depth-first search enumerates reduced words for the longest permutation $w_0$ by branching only on the even-indexed generators, using pruning constraints imposed by the geometry of optimal arrangements. The approach handles both perfect arrangements with a regular triangular pattern and unavoidable deviations from it for $n \\equiv 1 \\pmod 6$.\n  The output is classified into a hierarchy of equivalence classes: by commutation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29236","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/2607.29236/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":"2026-08-03T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZ+4GFGdSHMRpgfAYI6KTWHjXIKHwfzB5ZXjjdPLjDeFRe25aptyOlJgnTDmbBY4GNXMcQ1q2vbfoD6I8aMODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:41:36.278185Z"},"content_sha256":"0a38e0d55cc0dcbb9e485314c3d35fcd47d8002476ca8f7cf43f114feb9385da","schema_version":"1.0","event_id":"sha256:0a38e0d55cc0dcbb9e485314c3d35fcd47d8002476ca8f7cf43f114feb9385da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/bundle.json","state_url":"https://pith.science/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/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":"2026-08-04T15:41:36Z","links":{"resolver":"https://pith.science/pith/3Q4UIOR2VELXNTQIUXKN25IXXY","bundle":"https://pith.science/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/bundle.json","state":"https://pith.science/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3Q4UIOR2VELXNTQIUXKN25IXXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3Q4UIOR2VELXNTQIUXKN25IXXY","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":"29a2c82fb3a595ecec528cf408b5554d2993a34eebf7fcecdfe88957dd5de2a7","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-31T10:12:24Z","title_canon_sha256":"20a6f8711d3b363cb93db1e06b36ecf5262d7a3f9e0a1fb0cbec282afea8e2f1"},"schema_version":"1.0","source":{"id":"2607.29236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29236","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29236v1","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29236","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"3Q4UIOR2VELX","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_16","alias_value":"3Q4UIOR2VELXNTQI","created_at":"2026-08-03T01:22:25Z"},{"alias_kind":"pith_short_8","alias_value":"3Q4UIOR2","created_at":"2026-08-03T01:22:25Z"}],"graph_snapshots":[{"event_id":"sha256:0a38e0d55cc0dcbb9e485314c3d35fcd47d8002476ca8f7cf43f114feb9385da","target":"graph","created_at":"2026-08-03T01:22:25Z","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/2607.29236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe algorithms for the exhaustive enumeration and classification of simple arrangements of $n$ pseudolines ($n$ odd) maximizing the number of triangular faces. The depth-first search enumerates reduced words for the longest permutation $w_0$ by branching only on the even-indexed generators, using pruning constraints imposed by the geometry of optimal arrangements. The approach handles both perfect arrangements with a regular triangular pattern and unavoidable deviations from it for $n \\equiv 1 \\pmod 6$.\n  The output is classified into a hierarchy of equivalence classes: by commutation,","authors_text":"Denis Utkin, Roman Parpalak","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-31T10:12:24Z","title":"Enumeration and Classification of Triangle-Maximal Pseudoline Arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29236","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:b6efeee9994086e0ddac4c65557f43af9fc12190e42f6bf90a39e9a7a152be75","target":"record","created_at":"2026-08-03T01:22:25Z","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":"29a2c82fb3a595ecec528cf408b5554d2993a34eebf7fcecdfe88957dd5de2a7","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-31T10:12:24Z","title_canon_sha256":"20a6f8711d3b363cb93db1e06b36ecf5262d7a3f9e0a1fb0cbec282afea8e2f1"},"schema_version":"1.0","source":{"id":"2607.29236","kind":"arxiv","version":1}},"canonical_sha256":"dc39443a3aa91776ce08a5d4dd7517be0241a6ae96cb107c1d86a9f242a4c6a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc39443a3aa91776ce08a5d4dd7517be0241a6ae96cb107c1d86a9f242a4c6a0","first_computed_at":"2026-08-03T01:22:25.318449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:22:25.318449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTZmA1PP/yrOlv25l0ujH/F+hTUN7YJCVr7kLYMHTcqvqopbz3SZ9+L9Kms3yI70SVo4+8/darcKODrqQqMyCw==","signature_status":"signed_v1","signed_at":"2026-08-03T01:22:25.320086Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6efeee9994086e0ddac4c65557f43af9fc12190e42f6bf90a39e9a7a152be75","sha256:0a38e0d55cc0dcbb9e485314c3d35fcd47d8002476ca8f7cf43f114feb9385da"],"state_sha256":"b53c7dc8ad0d58939cf827c1c50c441d6ab299aa84cdb659e193e2ac98f4f00a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXO4KNwuJQ6DBgtCUBze/xwBnwoT26CNURYINQFI7/h9Gqr1YKF8bmsS4gkLfrsZHesmNsbLwTWiruXyoabrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:41:36.289304Z","bundle_sha256":"0e63fad13f8a351c52e4bf3410e0f1ce7b8e4bf2f9c7d3f7c473f27b8de17dee"}}