{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:G34GUCFWS2KL3PJJPB3MZFDXDU","short_pith_number":"pith:G34GUCFW","canonical_record":{"source":{"id":"2403.12713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-19T13:21:08Z","cross_cats_sorted":[],"title_canon_sha256":"d9f8d5973adc11580392f65d21a6bf5026f7581bb5056a5c814967050cccdca8","abstract_canon_sha256":"d0122979e0196be5bd4e2ba03e3d947890c22eeb04cba5dfd28108d1bda2c4b0"},"schema_version":"1.0"},"canonical_sha256":"36f86a08b69694bdbd297876cc94771d29efef78b100485c8abc3bfdfc1991d4","source":{"kind":"arxiv","id":"2403.12713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.12713","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"2403.12713v1","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.12713","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"G34GUCFWS2KL","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_16","alias_value":"G34GUCFWS2KL3PJJ","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_8","alias_value":"G34GUCFW","created_at":"2026-07-05T07:58:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:G34GUCFWS2KL3PJJPB3MZFDXDU","target":"record","payload":{"canonical_record":{"source":{"id":"2403.12713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-19T13:21:08Z","cross_cats_sorted":[],"title_canon_sha256":"d9f8d5973adc11580392f65d21a6bf5026f7581bb5056a5c814967050cccdca8","abstract_canon_sha256":"d0122979e0196be5bd4e2ba03e3d947890c22eeb04cba5dfd28108d1bda2c4b0"},"schema_version":"1.0"},"canonical_sha256":"36f86a08b69694bdbd297876cc94771d29efef78b100485c8abc3bfdfc1991d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:58:05.831546Z","signature_b64":"QHhoX6c5INpos1/m+a/zrAEfvbu6Bf2fdSCoOgPLBdoWYy96m/5W8g9F9rKH5wf4PgJL+6l7efYUjGK4l7GyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36f86a08b69694bdbd297876cc94771d29efef78b100485c8abc3bfdfc1991d4","last_reissued_at":"2026-07-05T07:58:05.831107Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:58:05.831107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.12713","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":"2026-07-05T07:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7xo1rILK/kqcU4/N0pQ6ElxSoIrWLTw82hnNTVHrWwYsFUplCq9hK7qFltZVABmcNlNevXuPdSaMjENi0QVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T18:18:50.648946Z"},"content_sha256":"4a679ab1310b6fcdb16f60da0219b4393231fb966519052f790bd49e2f812b70","schema_version":"1.0","event_id":"sha256:4a679ab1310b6fcdb16f60da0219b4393231fb966519052f790bd49e2f812b70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:G34GUCFWS2KL3PJJPB3MZFDXDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spanning Euler Tours in Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amin Bahmanian, Songling Shan","submitted_at":"2024-03-19T13:21:08Z","abstract_excerpt":"Motivated by generalizations of de Bruijn cycles to various combinatorial structures (Chung, Diaconis, and Graham), we study various Euler tours in set systems. Let $\\mathcal{G}$ be a hypergraph whose corank and rank are $c\\geq 3$ and $k$, respetively. The minimum $t$-degree of $\\mathcal{G}$ is the fewest number of edges containing every $t$-subset of vertices. An Euler tour (family, respectively) in $\\mathcal{G}$ is a (family of, respectively) closed walk(s) that (jointly, respectively) traverses each edge of $\\mathcal{G}$ exactly once. An Euler tour is spanning if it traverses all the vertic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.12713","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.12713/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGhMYSAFlGXkeDrCJaduwzWxy8MzeGSitFJzwjFUVEwF5vvzwQjoc5pNqiip2GKLg9CwuZdDNovuUT8qt4XaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T18:18:50.649751Z"},"content_sha256":"7ffca53c74e5d95454c65c2ade2c9f0e1303d2e978ed320857959953eb7ac245","schema_version":"1.0","event_id":"sha256:7ffca53c74e5d95454c65c2ade2c9f0e1303d2e978ed320857959953eb7ac245"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/bundle.json","state_url":"https://pith.science/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/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":"2026-08-23T18:18:50Z","links":{"resolver":"https://pith.science/pith/G34GUCFWS2KL3PJJPB3MZFDXDU","bundle":"https://pith.science/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/bundle.json","state":"https://pith.science/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G34GUCFWS2KL3PJJPB3MZFDXDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G34GUCFWS2KL3PJJPB3MZFDXDU","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":"d0122979e0196be5bd4e2ba03e3d947890c22eeb04cba5dfd28108d1bda2c4b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-19T13:21:08Z","title_canon_sha256":"d9f8d5973adc11580392f65d21a6bf5026f7581bb5056a5c814967050cccdca8"},"schema_version":"1.0","source":{"id":"2403.12713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.12713","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"2403.12713v1","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.12713","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"G34GUCFWS2KL","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_16","alias_value":"G34GUCFWS2KL3PJJ","created_at":"2026-07-05T07:58:05Z"},{"alias_kind":"pith_short_8","alias_value":"G34GUCFW","created_at":"2026-07-05T07:58:05Z"}],"graph_snapshots":[{"event_id":"sha256:7ffca53c74e5d95454c65c2ade2c9f0e1303d2e978ed320857959953eb7ac245","target":"graph","created_at":"2026-07-05T07:58:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.12713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by generalizations of de Bruijn cycles to various combinatorial structures (Chung, Diaconis, and Graham), we study various Euler tours in set systems. Let $\\mathcal{G}$ be a hypergraph whose corank and rank are $c\\geq 3$ and $k$, respetively. The minimum $t$-degree of $\\mathcal{G}$ is the fewest number of edges containing every $t$-subset of vertices. An Euler tour (family, respectively) in $\\mathcal{G}$ is a (family of, respectively) closed walk(s) that (jointly, respectively) traverses each edge of $\\mathcal{G}$ exactly once. An Euler tour is spanning if it traverses all the vertic","authors_text":"Amin Bahmanian, Songling Shan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-19T13:21:08Z","title":"Spanning Euler Tours in Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.12713","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":"sha256:4a679ab1310b6fcdb16f60da0219b4393231fb966519052f790bd49e2f812b70","target":"record","created_at":"2026-07-05T07:58:05Z","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":"d0122979e0196be5bd4e2ba03e3d947890c22eeb04cba5dfd28108d1bda2c4b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-19T13:21:08Z","title_canon_sha256":"d9f8d5973adc11580392f65d21a6bf5026f7581bb5056a5c814967050cccdca8"},"schema_version":"1.0","source":{"id":"2403.12713","kind":"arxiv","version":1}},"canonical_sha256":"36f86a08b69694bdbd297876cc94771d29efef78b100485c8abc3bfdfc1991d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36f86a08b69694bdbd297876cc94771d29efef78b100485c8abc3bfdfc1991d4","first_computed_at":"2026-07-05T07:58:05.831107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:58:05.831107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QHhoX6c5INpos1/m+a/zrAEfvbu6Bf2fdSCoOgPLBdoWYy96m/5W8g9F9rKH5wf4PgJL+6l7efYUjGK4l7GyBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:58:05.831546Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.12713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a679ab1310b6fcdb16f60da0219b4393231fb966519052f790bd49e2f812b70","sha256:7ffca53c74e5d95454c65c2ade2c9f0e1303d2e978ed320857959953eb7ac245"],"state_sha256":"b3785d6dbb00368e587c1b9dc861336876349cf12683c94ab1843b2d7b2d9267"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"laf40StGeY6thmO6xpzGyBNwlyykMApAUcN0wEaheLJsbkXZXdUDUN++wPHrfVcm6Kd4D5n9E+AzoqZlSQq4AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T18:18:50.654159Z","bundle_sha256":"ca0954b0a87a7742c0f7cfaba71a3be76889c641cfd89fc8171bf04881d44689"}}