{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UWRAQCYGVOVEVBLMJJIL6NUKWG","short_pith_number":"pith:UWRAQCYG","canonical_record":{"source":{"id":"1507.05306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"ab84b2331f7043fae17713effc2bd9efa9dc565666ce0f2bc6a5b49ba7febcba","abstract_canon_sha256":"536c89d681be94a83b2d62b594343eecb87f17ea2b83f3488e791e010f0efd21"},"schema_version":"1.0"},"canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","source":{"kind":"arxiv","id":"1507.05306","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05306","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05306v1","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05306","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"UWRAQCYGVOVE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UWRAQCYGVOVEVBLM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UWRAQCYG","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UWRAQCYGVOVEVBLMJJIL6NUKWG","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"ab84b2331f7043fae17713effc2bd9efa9dc565666ce0f2bc6a5b49ba7febcba","abstract_canon_sha256":"536c89d681be94a83b2d62b594343eecb87f17ea2b83f3488e791e010f0efd21"},"schema_version":"1.0"},"canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:37.243947Z","signature_b64":"Ft9PYjKFUFMj0yuWKzsfJR97W6/+jQYvVcaCu7wkCTY2tRHuVDLCQCpIc3Kac8czaouGaCGUt9ufoFfHDPysCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","last_reissued_at":"2026-05-18T01:36:37.243202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:37.243202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05306","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":"2026-05-18T01:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5tqniStf0bBlWDul6zSED8ODgCH4ZpvqzuEA37dfrVJvvlGHLNyJK5JL21Wa8jBUBsXxTB7XebofIiABa8dCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:18:14.700148Z"},"content_sha256":"ef32b5b880224ee058e09e17b7927a4cb2defd12df1366522fc702225a3dd5e0","schema_version":"1.0","event_id":"sha256:ef32b5b880224ee058e09e17b7927a4cb2defd12df1366522fc702225a3dd5e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UWRAQCYGVOVEVBLMJJIL6NUKWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of a conjecture on monomial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Lazebnik, Stephen D. Lappano, Xiang-dong Hou","submitted_at":"2015-07-19T16:50:14Z","abstract_excerpt":"Let $e$ be a positive integer, $p$ be an odd prime, $q=p^{e}$, and $\\Bbb F_q$ be the finite field of $q$ elements. Let $f,g \\in \\Bbb F_q [X,Y]$. The graph $G=G_q(f,g)$ is a bipartite graph with vertex partitions $P=\\Bbb F_q^3$ and $L=\\Bbb F_q^3$, and edges defined as follows: a vertex $(p)=(p_1,p_2,p_3)\\in P$ is adjacent to a vertex $[l] = [l_1,l_2,l_3]\\in L$ if and only if $p_2 + l_2 = f(p_1,l_1)$ and $p_3 + l_3 = g(p_1,l_1)$. Motivated by some questions in finite geometry and extremal graph theory, Dmytrenko, Lazebnik and Williford conjectured in 2007 that if $f$ and $g$ are both monomials a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05306","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":""},"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":"2026-05-18T01:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8iJckiaFEl5MqrjPAoGjaXPpwaKiWaJ0DXanZ3P63F6hKXfZX2WhZZAw4QHQVQtRLxo0ENCb5PhWWvdQKqMJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:18:14.700541Z"},"content_sha256":"3657e03e09dd49e0424de988895ee9b4ebca83ba62f81f01da61cabce72f38fd","schema_version":"1.0","event_id":"sha256:3657e03e09dd49e0424de988895ee9b4ebca83ba62f81f01da61cabce72f38fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/bundle.json","state_url":"https://pith.science/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/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":"2026-06-01T04:18:14Z","links":{"resolver":"https://pith.science/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG","bundle":"https://pith.science/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/bundle.json","state":"https://pith.science/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWRAQCYGVOVEVBLMJJIL6NUKWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UWRAQCYGVOVEVBLMJJIL6NUKWG","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":"536c89d681be94a83b2d62b594343eecb87f17ea2b83f3488e791e010f0efd21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","title_canon_sha256":"ab84b2331f7043fae17713effc2bd9efa9dc565666ce0f2bc6a5b49ba7febcba"},"schema_version":"1.0","source":{"id":"1507.05306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05306","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05306v1","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05306","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"UWRAQCYGVOVE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UWRAQCYGVOVEVBLM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UWRAQCYG","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:3657e03e09dd49e0424de988895ee9b4ebca83ba62f81f01da61cabce72f38fd","target":"graph","created_at":"2026-05-18T01:36:37Z","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":"Let $e$ be a positive integer, $p$ be an odd prime, $q=p^{e}$, and $\\Bbb F_q$ be the finite field of $q$ elements. Let $f,g \\in \\Bbb F_q [X,Y]$. The graph $G=G_q(f,g)$ is a bipartite graph with vertex partitions $P=\\Bbb F_q^3$ and $L=\\Bbb F_q^3$, and edges defined as follows: a vertex $(p)=(p_1,p_2,p_3)\\in P$ is adjacent to a vertex $[l] = [l_1,l_2,l_3]\\in L$ if and only if $p_2 + l_2 = f(p_1,l_1)$ and $p_3 + l_3 = g(p_1,l_1)$. Motivated by some questions in finite geometry and extremal graph theory, Dmytrenko, Lazebnik and Williford conjectured in 2007 that if $f$ and $g$ are both monomials a","authors_text":"Felix Lazebnik, Stephen D. Lappano, Xiang-dong Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","title":"Proof of a conjecture on monomial graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05306","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:ef32b5b880224ee058e09e17b7927a4cb2defd12df1366522fc702225a3dd5e0","target":"record","created_at":"2026-05-18T01:36:37Z","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":"536c89d681be94a83b2d62b594343eecb87f17ea2b83f3488e791e010f0efd21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","title_canon_sha256":"ab84b2331f7043fae17713effc2bd9efa9dc565666ce0f2bc6a5b49ba7febcba"},"schema_version":"1.0","source":{"id":"1507.05306","kind":"arxiv","version":1}},"canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","first_computed_at":"2026-05-18T01:36:37.243202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:37.243202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ft9PYjKFUFMj0yuWKzsfJR97W6/+jQYvVcaCu7wkCTY2tRHuVDLCQCpIc3Kac8czaouGaCGUt9ufoFfHDPysCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:37.243947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef32b5b880224ee058e09e17b7927a4cb2defd12df1366522fc702225a3dd5e0","sha256:3657e03e09dd49e0424de988895ee9b4ebca83ba62f81f01da61cabce72f38fd"],"state_sha256":"8979ed5bcb42d53cfaa165c30b57795e3f2b0683f8c60396f783c1332fc8b1b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CCfzZ+bwaPflFqelfhiyvC+DDfCgFpc90kI6rUJRqc99it1sulIrmWaHBWfv8E6KGdaeUAuzxbg0PK2z2FPODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:18:14.702742Z","bundle_sha256":"193eef126077a7f6a53e51c75d7e8b667f9962af7e75606a81b3df39f53c73cb"}}