{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JDKGHUDO4CPDSFDJBXYDE6XTKJ","short_pith_number":"pith:JDKGHUDO","canonical_record":{"source":{"id":"1405.2761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-12T13:59:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b0739db7477b34dcdfc84b243d7adbe547d3e8ca918639b77f29ef27e79bf992","abstract_canon_sha256":"e4150305bc487bb7eacdf9fe3d7bddafb47c3e58f90b3d5d46ee95a8eac354b0"},"schema_version":"1.0"},"canonical_sha256":"48d463d06ee09e3914690df0327af35260700f2c927187529bb049d3f365baaa","source":{"kind":"arxiv","id":"1405.2761","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2761","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2761v1","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2761","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"JDKGHUDO4CPD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDKGHUDO4CPDSFDJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDKGHUDO","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JDKGHUDO4CPDSFDJBXYDE6XTKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-12T13:59:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b0739db7477b34dcdfc84b243d7adbe547d3e8ca918639b77f29ef27e79bf992","abstract_canon_sha256":"e4150305bc487bb7eacdf9fe3d7bddafb47c3e58f90b3d5d46ee95a8eac354b0"},"schema_version":"1.0"},"canonical_sha256":"48d463d06ee09e3914690df0327af35260700f2c927187529bb049d3f365baaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.526089Z","signature_b64":"P2TQV4wZ2DOq+BjT4yBBtJpbIznvyO4Yq5nKsTxoECP3L0agSI+wGPGVRs2wCFjd6Pge1vxa4LbDPwYM3FHVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48d463d06ee09e3914690df0327af35260700f2c927187529bb049d3f365baaa","last_reissued_at":"2026-05-18T01:34:13.525402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.525402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2761","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":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eic1gyIaQEULEkQax7pbxUpSMbkoHOGCtn6GyySutVmwkc/qg2xO/DdFyAOINBdaC6VfGISiokm7rcYjmsaaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:22:54.929049Z"},"content_sha256":"abd3499c874f9bf1427154160fd8ebc7500be3b9836f99de30cf59182336efe9","schema_version":"1.0","event_id":"sha256:abd3499c874f9bf1427154160fd8ebc7500be3b9836f99de30cf59182336efe9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JDKGHUDO4CPDSFDJBXYDE6XTKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite primitive and distance transitive directed graphs of finite out-valency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Daniela Amato, David M. Evans","submitted_at":"2014-05-12T13:59:46Z","abstract_excerpt":"We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2761","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":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAcaLoaPn9qcWw43ZDnCSS8/MiAHp6O2UxoqAdZPdO1n6EBU+5smYGj3Cpy3fhrEJVAzBN5BZJ5ICp3Vo22GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:22:54.929704Z"},"content_sha256":"d1cd896171dadf55c4abf2011308579e40c1fd17d641c5fd3110056c0cbedf4f","schema_version":"1.0","event_id":"sha256:d1cd896171dadf55c4abf2011308579e40c1fd17d641c5fd3110056c0cbedf4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/bundle.json","state_url":"https://pith.science/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/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":"2026-05-19T23:22:54Z","links":{"resolver":"https://pith.science/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ","bundle":"https://pith.science/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/bundle.json","state":"https://pith.science/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDKGHUDO4CPDSFDJBXYDE6XTKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JDKGHUDO4CPDSFDJBXYDE6XTKJ","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":"e4150305bc487bb7eacdf9fe3d7bddafb47c3e58f90b3d5d46ee95a8eac354b0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-12T13:59:46Z","title_canon_sha256":"b0739db7477b34dcdfc84b243d7adbe547d3e8ca918639b77f29ef27e79bf992"},"schema_version":"1.0","source":{"id":"1405.2761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2761","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2761v1","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2761","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"JDKGHUDO4CPD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDKGHUDO4CPDSFDJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDKGHUDO","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d1cd896171dadf55c4abf2011308579e40c1fd17d641c5fd3110056c0cbedf4f","target":"graph","created_at":"2026-05-18T01:34:13Z","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 give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph.","authors_text":"Daniela Amato, David M. Evans","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-12T13:59:46Z","title":"Infinite primitive and distance transitive directed graphs of finite out-valency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2761","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:abd3499c874f9bf1427154160fd8ebc7500be3b9836f99de30cf59182336efe9","target":"record","created_at":"2026-05-18T01:34:13Z","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":"e4150305bc487bb7eacdf9fe3d7bddafb47c3e58f90b3d5d46ee95a8eac354b0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-12T13:59:46Z","title_canon_sha256":"b0739db7477b34dcdfc84b243d7adbe547d3e8ca918639b77f29ef27e79bf992"},"schema_version":"1.0","source":{"id":"1405.2761","kind":"arxiv","version":1}},"canonical_sha256":"48d463d06ee09e3914690df0327af35260700f2c927187529bb049d3f365baaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48d463d06ee09e3914690df0327af35260700f2c927187529bb049d3f365baaa","first_computed_at":"2026-05-18T01:34:13.525402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:13.525402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P2TQV4wZ2DOq+BjT4yBBtJpbIznvyO4Yq5nKsTxoECP3L0agSI+wGPGVRs2wCFjd6Pge1vxa4LbDPwYM3FHVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:13.526089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abd3499c874f9bf1427154160fd8ebc7500be3b9836f99de30cf59182336efe9","sha256:d1cd896171dadf55c4abf2011308579e40c1fd17d641c5fd3110056c0cbedf4f"],"state_sha256":"f011efb88ff41710cd767fb25f3dd0506c280cae914589f92132e78c5caafb82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9WeSV+nhaGQPhdJ8mfDqi3W4ncUdtmaAld6FFXYjuUqMi0VUGWAPka3ANf5KpAuXcYW9TaQ1fwnWGdWv3LvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T23:22:54.933495Z","bundle_sha256":"d7ae1f8ac26ecb2748fe89950d0ad6b66812fa32bb8c6b1da63c3ace998315dc"}}