{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VXZYNSAI7BYVNAMAOVGJJWBMSK","short_pith_number":"pith:VXZYNSAI","canonical_record":{"source":{"id":"1807.11362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","cross_cats_sorted":[],"title_canon_sha256":"98bae4000a48907836cd87579da0da1b4b6d99197ee3f246d3c787102145faef","abstract_canon_sha256":"9926b92904b2262ad3986e6c75d219286532d588eabb51a94966e8d0af140f86"},"schema_version":"1.0"},"canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","source":{"kind":"arxiv","id":"1807.11362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11362","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11362v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11362","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"VXZYNSAI7BYV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXZYNSAI7BYVNAMA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXZYNSAI","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VXZYNSAI7BYVNAMAOVGJJWBMSK","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","cross_cats_sorted":[],"title_canon_sha256":"98bae4000a48907836cd87579da0da1b4b6d99197ee3f246d3c787102145faef","abstract_canon_sha256":"9926b92904b2262ad3986e6c75d219286532d588eabb51a94966e8d0af140f86"},"schema_version":"1.0"},"canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.102652Z","signature_b64":"AGXgRqBz2nv7sjobZre4FUXk1JO2xBxbEyTgvDq8rz0gb71jCZl7ztYDWsXQM1NeFFYrEDRN/+RxFuhuVn0tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","last_reissued_at":"2026-05-18T00:09:32.102103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.102103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11362","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JS+FH9V/XKTYl7AUmz9ROBedSR5TsN0rqJzf8HLA8pjluNCSp6xneK09Ti06OdwITl4ConniEK7yY3ygVWWLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:35:04.840229Z"},"content_sha256":"032747e7c89bebccb85c72eabea171fb1b790fc5c985a4f2dee046314cada32d","schema_version":"1.0","event_id":"sha256:032747e7c89bebccb85c72eabea171fb1b790fc5c985a4f2dee046314cada32d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VXZYNSAI7BYVNAMAOVGJJWBMSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on the Isomorphism Problem for Monomial Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Kodess, Felix Lazebnik","submitted_at":"2018-07-30T14:12:20Z","abstract_excerpt":"Let $p$ be a prime $e$ be a positive integer, $q = p^e$, and let $\\mathbb{F}_q$ denote the finite field of $q$ elements. Let $m,n$, $1\\le m,n\\le q-1$, be integers. The monomial digraph $D= D(q;m,n)$ is defined as follows: the vertex set of $D$ is $\\mathbb{F}_q^2$, and $((x_1,x_2),(y_1,y_2))$ is an arc in $D$ if $ x_2 + y_2 = x_1^m y_1^n $. In this note we study the question of isomorphism of monomial digraphs $D(q;m_1,n_1)$ and $D(q;m_2,n_2)$. Several necessary conditions and several sufficient conditions for the isomorphism are found. We conjecture that one simple sufficient condition is also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11362","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciwtlsZZKdGjAhIo9b2MbIrDJDI2A010nvcC4PwGggPekaYSLEw4mzvc+KoGhfyOVgv3X1ptbyUlxIXgYBjdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:35:04.840908Z"},"content_sha256":"bdb64ec7540d4045102793261ff0f27cbfc255d71b37679a6f09a05365ae4ad2","schema_version":"1.0","event_id":"sha256:bdb64ec7540d4045102793261ff0f27cbfc255d71b37679a6f09a05365ae4ad2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/bundle.json","state_url":"https://pith.science/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/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":"2026-05-26T18:35:04Z","links":{"resolver":"https://pith.science/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK","bundle":"https://pith.science/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/bundle.json","state":"https://pith.science/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXZYNSAI7BYVNAMAOVGJJWBMSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VXZYNSAI7BYVNAMAOVGJJWBMSK","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":"9926b92904b2262ad3986e6c75d219286532d588eabb51a94966e8d0af140f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","title_canon_sha256":"98bae4000a48907836cd87579da0da1b4b6d99197ee3f246d3c787102145faef"},"schema_version":"1.0","source":{"id":"1807.11362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11362","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11362v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11362","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"VXZYNSAI7BYV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXZYNSAI7BYVNAMA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXZYNSAI","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:bdb64ec7540d4045102793261ff0f27cbfc255d71b37679a6f09a05365ae4ad2","target":"graph","created_at":"2026-05-18T00:09:32Z","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 $p$ be a prime $e$ be a positive integer, $q = p^e$, and let $\\mathbb{F}_q$ denote the finite field of $q$ elements. Let $m,n$, $1\\le m,n\\le q-1$, be integers. The monomial digraph $D= D(q;m,n)$ is defined as follows: the vertex set of $D$ is $\\mathbb{F}_q^2$, and $((x_1,x_2),(y_1,y_2))$ is an arc in $D$ if $ x_2 + y_2 = x_1^m y_1^n $. In this note we study the question of isomorphism of monomial digraphs $D(q;m_1,n_1)$ and $D(q;m_2,n_2)$. Several necessary conditions and several sufficient conditions for the isomorphism are found. We conjecture that one simple sufficient condition is also","authors_text":"Alex Kodess, Felix Lazebnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","title":"A Note on the Isomorphism Problem for Monomial Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11362","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":"sha256:032747e7c89bebccb85c72eabea171fb1b790fc5c985a4f2dee046314cada32d","target":"record","created_at":"2026-05-18T00:09:32Z","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":"9926b92904b2262ad3986e6c75d219286532d588eabb51a94966e8d0af140f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","title_canon_sha256":"98bae4000a48907836cd87579da0da1b4b6d99197ee3f246d3c787102145faef"},"schema_version":"1.0","source":{"id":"1807.11362","kind":"arxiv","version":1}},"canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","first_computed_at":"2026-05-18T00:09:32.102103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.102103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AGXgRqBz2nv7sjobZre4FUXk1JO2xBxbEyTgvDq8rz0gb71jCZl7ztYDWsXQM1NeFFYrEDRN/+RxFuhuVn0tAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.102652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:032747e7c89bebccb85c72eabea171fb1b790fc5c985a4f2dee046314cada32d","sha256:bdb64ec7540d4045102793261ff0f27cbfc255d71b37679a6f09a05365ae4ad2"],"state_sha256":"8cc733250edeff0308b8433965a0c68539f11109a999906a492330e62e3bf779"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53JqZZnfM04UVW3YLbhUuIs3EsWNVAF4vsoBY1pOWy4sWBeFkU0+Urhp9i7P2G2MNJuIatzUotXb0gqdFL/jDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:35:04.844232Z","bundle_sha256":"e0470f2abd77ce98f539b98d669f509ce9f1a19617d7cfa43494e477e01233b0"}}