{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FVGPZE5U4KFFYYNYZR23OYJPKR","short_pith_number":"pith:FVGPZE5U","canonical_record":{"source":{"id":"1507.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T02:41:32Z","cross_cats_sorted":[],"title_canon_sha256":"54771bf275d82538f53e4ae6f4f88983cda539aafc660aabd27e007e344465ea","abstract_canon_sha256":"bb9fc14a68c93bb903ebc88c28567a51d0b28036c44a3e0c4e675ce6e00a80be"},"schema_version":"1.0"},"canonical_sha256":"2d4cfc93b4e28a5c61b8cc75b7612f5454bdfe46b8c8468645bdd3bfa82371e3","source":{"kind":"arxiv","id":"1507.03705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03705","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03705v1","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03705","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"FVGPZE5U4KFF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FVGPZE5U4KFFYYNY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FVGPZE5U","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FVGPZE5U4KFFYYNYZR23OYJPKR","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T02:41:32Z","cross_cats_sorted":[],"title_canon_sha256":"54771bf275d82538f53e4ae6f4f88983cda539aafc660aabd27e007e344465ea","abstract_canon_sha256":"bb9fc14a68c93bb903ebc88c28567a51d0b28036c44a3e0c4e675ce6e00a80be"},"schema_version":"1.0"},"canonical_sha256":"2d4cfc93b4e28a5c61b8cc75b7612f5454bdfe46b8c8468645bdd3bfa82371e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:57.531616Z","signature_b64":"QMLFwDpjr5YOu/difhWiC6VgIg1+43WKiq+2n2gVAVNnGlTUacmVtGDBFnJJLC9ZmeH2MKRBqg0tL9ONkyJ7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d4cfc93b4e28a5c61b8cc75b7612f5454bdfe46b8c8468645bdd3bfa82371e3","last_reissued_at":"2026-05-18T01:36:57.531066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:57.531066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03705","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":"2026-05-18T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bt3kJ+KYu2rDiIVmCjmM6NDDSHF7761F3P9rAg8+sYWKCeINeK9zzlciYBh1VK07FroM/S9ox7VwqwzP+C9bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:00:23.509520Z"},"content_sha256":"77dfbc071d1852f11a257070c0a9b7e5b357b63a9f2adf22a6327782d61f4ad5","schema_version":"1.0","event_id":"sha256:77dfbc071d1852f11a257070c0a9b7e5b357b63a9f2adf22a6327782d61f4ad5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FVGPZE5U4KFFYYNYZR23OYJPKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite Orders and Non-$D$-finite Property of $3$-Dimensional Lattice Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel K. Du, Qing-Hu Hou, Rong-Hua Wang","submitted_at":"2015-07-14T02:41:32Z","abstract_excerpt":"Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant $\\mathbb{N}^3$. For the $35548$ non-trivial models with at most six steps, they found that many models associated to a group of order at least $200$ and conjectured these groups were in fact infinite groups. In this paper, we first confirm these conjectures and then consider the non-$D$-finite property of the generating function for some of these models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03705","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":"2026-05-18T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5Rlg2pKoWzQYjDJbVajhNfQN1q7wqA7cYLOQ8id9ZlCZ5xEiC8wBe6V11kFKp5mZ1cuRYMigZzOLizJ5z1SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:00:23.509866Z"},"content_sha256":"398b0d66042fa24152291e5b8d9041a8794ddcef943c24ae1deb6b03a5111404","schema_version":"1.0","event_id":"sha256:398b0d66042fa24152291e5b8d9041a8794ddcef943c24ae1deb6b03a5111404"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/bundle.json","state_url":"https://pith.science/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/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":"2026-06-02T04:00:23Z","links":{"resolver":"https://pith.science/pith/FVGPZE5U4KFFYYNYZR23OYJPKR","bundle":"https://pith.science/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/bundle.json","state":"https://pith.science/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVGPZE5U4KFFYYNYZR23OYJPKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FVGPZE5U4KFFYYNYZR23OYJPKR","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":"bb9fc14a68c93bb903ebc88c28567a51d0b28036c44a3e0c4e675ce6e00a80be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T02:41:32Z","title_canon_sha256":"54771bf275d82538f53e4ae6f4f88983cda539aafc660aabd27e007e344465ea"},"schema_version":"1.0","source":{"id":"1507.03705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03705","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03705v1","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03705","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"FVGPZE5U4KFF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FVGPZE5U4KFFYYNY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FVGPZE5U","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:398b0d66042fa24152291e5b8d9041a8794ddcef943c24ae1deb6b03a5111404","target":"graph","created_at":"2026-05-18T01:36:57Z","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":"Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant $\\mathbb{N}^3$. For the $35548$ non-trivial models with at most six steps, they found that many models associated to a group of order at least $200$ and conjectured these groups were in fact infinite groups. In this paper, we first confirm these conjectures and then consider the non-$D$-finite property of the generating function for some of these models.","authors_text":"Daniel K. Du, Qing-Hu Hou, Rong-Hua Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T02:41:32Z","title":"Infinite Orders and Non-$D$-finite Property of $3$-Dimensional Lattice Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03705","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":"sha256:77dfbc071d1852f11a257070c0a9b7e5b357b63a9f2adf22a6327782d61f4ad5","target":"record","created_at":"2026-05-18T01:36:57Z","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":"bb9fc14a68c93bb903ebc88c28567a51d0b28036c44a3e0c4e675ce6e00a80be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T02:41:32Z","title_canon_sha256":"54771bf275d82538f53e4ae6f4f88983cda539aafc660aabd27e007e344465ea"},"schema_version":"1.0","source":{"id":"1507.03705","kind":"arxiv","version":1}},"canonical_sha256":"2d4cfc93b4e28a5c61b8cc75b7612f5454bdfe46b8c8468645bdd3bfa82371e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d4cfc93b4e28a5c61b8cc75b7612f5454bdfe46b8c8468645bdd3bfa82371e3","first_computed_at":"2026-05-18T01:36:57.531066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:57.531066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QMLFwDpjr5YOu/difhWiC6VgIg1+43WKiq+2n2gVAVNnGlTUacmVtGDBFnJJLC9ZmeH2MKRBqg0tL9ONkyJ7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:57.531616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77dfbc071d1852f11a257070c0a9b7e5b357b63a9f2adf22a6327782d61f4ad5","sha256:398b0d66042fa24152291e5b8d9041a8794ddcef943c24ae1deb6b03a5111404"],"state_sha256":"e5b778987b1e0614ee73ac1e8b82a05456cb0a4b1404f4ebc21827b08ae605a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ExlH+VyZVaJoG93WnycFIi3TfwXM+ud9kqpQrDSXMuDVFKRZkzR5FCn0TNhu/9GAdpF57CdHQxdpHg4dEpdCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:00:23.511780Z","bundle_sha256":"041732965a5ff345fa2379943575e8011466a89c05fbda1c90ecf96057a8c3c1"}}