{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L3ELUOI3NW5GNFMNGDFUVW6K65","short_pith_number":"pith:L3ELUOI3","canonical_record":{"source":{"id":"1810.09954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T16:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"5fab429b6cb7d8917366d49297119659360c02fd08ce0fde50e7f3df88f9c221","abstract_canon_sha256":"57c0ddaee038924909207332e32fb9393889387ff96563139f4e2a7710dc0c0b"},"schema_version":"1.0"},"canonical_sha256":"5ec8ba391b6dba66958d30cb4adbcaf778264b2afabf23594d28c6db9a334802","source":{"kind":"arxiv","id":"1810.09954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09954","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09954v1","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09954","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"L3ELUOI3NW5G","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L3ELUOI3NW5GNFMN","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L3ELUOI3","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L3ELUOI3NW5GNFMNGDFUVW6K65","target":"record","payload":{"canonical_record":{"source":{"id":"1810.09954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T16:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"5fab429b6cb7d8917366d49297119659360c02fd08ce0fde50e7f3df88f9c221","abstract_canon_sha256":"57c0ddaee038924909207332e32fb9393889387ff96563139f4e2a7710dc0c0b"},"schema_version":"1.0"},"canonical_sha256":"5ec8ba391b6dba66958d30cb4adbcaf778264b2afabf23594d28c6db9a334802","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:28.824436Z","signature_b64":"IOrOzfJeDVkBJ58izi+/5x84Cf6LIkmVr/kB2akGrtS9krVW5TsD2ndLBCsPM5dKNm7anoVIsC9jm4AT7YmIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ec8ba391b6dba66958d30cb4adbcaf778264b2afabf23594d28c6db9a334802","last_reissued_at":"2026-05-18T00:02:28.823814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:28.823814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.09954","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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dCGZiIwpou13U9wbL9iv4T+ijgbBa5cdV/8cbrMtY//S/5ihdPr0cMrUCn9tm3SkFNbXmVIG6gC9JITZlqoTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:40:25.766630Z"},"content_sha256":"bbb0227d6a65d3c76ea85c5fcc80855ecd4e5725da6906d4d09e52675948e12e","schema_version":"1.0","event_id":"sha256:bbb0227d6a65d3c76ea85c5fcc80855ecd4e5725da6906d4d09e52675948e12e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L3ELUOI3NW5GNFMNGDFUVW6K65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharply $k$-arc-transitive-digraphs: finite and infinite examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) University of Ljubljana, (3) Montanuniversit\\\"at Leoben, Austria), Iceland, Ljubljana, Norbert Seifter (3) ((1) University of Iceland, Primo\\v{z} Poto\\v{c}nik (2), Reykjav\\'ik, R\\\"ognvaldur G. M\\\"oller (1), Slovenia","submitted_at":"2018-10-23T16:36:09Z","abstract_excerpt":"A general method for constructing sharply $k$-arc-transitive digraphs, i.e. digraphs that are $k$-arc-transitive but not $(k+1)$-arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples. The infinite examples can have one, two or infinitely many ends. Among the one-ended examples there are also digraphs that have polynomial growth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09954","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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wenI5xxFD7zfhk3TB/+NzDFFr8jYi2tc6Y507gf7EcFfSrqZXvLJICysLjuDOLS4tE4v2rungDDUkWziucJ9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:40:25.766966Z"},"content_sha256":"3152db9398bc9ff4edba95fef6f1211d13eeafeed310c8ca15acb3b845ffa436","schema_version":"1.0","event_id":"sha256:3152db9398bc9ff4edba95fef6f1211d13eeafeed310c8ca15acb3b845ffa436"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/bundle.json","state_url":"https://pith.science/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/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":"2026-06-01T23:40:25Z","links":{"resolver":"https://pith.science/pith/L3ELUOI3NW5GNFMNGDFUVW6K65","bundle":"https://pith.science/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/bundle.json","state":"https://pith.science/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3ELUOI3NW5GNFMNGDFUVW6K65/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L3ELUOI3NW5GNFMNGDFUVW6K65","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":"57c0ddaee038924909207332e32fb9393889387ff96563139f4e2a7710dc0c0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T16:36:09Z","title_canon_sha256":"5fab429b6cb7d8917366d49297119659360c02fd08ce0fde50e7f3df88f9c221"},"schema_version":"1.0","source":{"id":"1810.09954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09954","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09954v1","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09954","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"L3ELUOI3NW5G","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L3ELUOI3NW5GNFMN","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L3ELUOI3","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:3152db9398bc9ff4edba95fef6f1211d13eeafeed310c8ca15acb3b845ffa436","target":"graph","created_at":"2026-05-18T00:02:28Z","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":"A general method for constructing sharply $k$-arc-transitive digraphs, i.e. digraphs that are $k$-arc-transitive but not $(k+1)$-arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples. The infinite examples can have one, two or infinitely many ends. Among the one-ended examples there are also digraphs that have polynomial growth.","authors_text":"(2) University of Ljubljana, (3) Montanuniversit\\\"at Leoben, Austria), Iceland, Ljubljana, Norbert Seifter (3) ((1) University of Iceland, Primo\\v{z} Poto\\v{c}nik (2), Reykjav\\'ik, R\\\"ognvaldur G. M\\\"oller (1), Slovenia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T16:36:09Z","title":"Sharply $k$-arc-transitive-digraphs: finite and infinite examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09954","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:bbb0227d6a65d3c76ea85c5fcc80855ecd4e5725da6906d4d09e52675948e12e","target":"record","created_at":"2026-05-18T00:02:28Z","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":"57c0ddaee038924909207332e32fb9393889387ff96563139f4e2a7710dc0c0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T16:36:09Z","title_canon_sha256":"5fab429b6cb7d8917366d49297119659360c02fd08ce0fde50e7f3df88f9c221"},"schema_version":"1.0","source":{"id":"1810.09954","kind":"arxiv","version":1}},"canonical_sha256":"5ec8ba391b6dba66958d30cb4adbcaf778264b2afabf23594d28c6db9a334802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ec8ba391b6dba66958d30cb4adbcaf778264b2afabf23594d28c6db9a334802","first_computed_at":"2026-05-18T00:02:28.823814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:28.823814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IOrOzfJeDVkBJ58izi+/5x84Cf6LIkmVr/kB2akGrtS9krVW5TsD2ndLBCsPM5dKNm7anoVIsC9jm4AT7YmIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:28.824436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb0227d6a65d3c76ea85c5fcc80855ecd4e5725da6906d4d09e52675948e12e","sha256:3152db9398bc9ff4edba95fef6f1211d13eeafeed310c8ca15acb3b845ffa436"],"state_sha256":"3727747c07554de3de973c8c241442e586023d65544312740db195d3ec90c29e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFtkG/y/KfrgJ+Q8ZetBboEnOvQPw8lOrzSN/S9SXDIp5QzaXaBYPsvDwZvQ54/5GhVX4gFtfiNUN4/OTTLnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:40:25.768946Z","bundle_sha256":"61e491ae0f3c5cd22bdb7c6fd50743739df1973127b25aba108ab2a1666c87e8"}}