{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IPGLXUO26CIAYP5Q2UNUA2KOYP","short_pith_number":"pith:IPGLXUO2","canonical_record":{"source":{"id":"2605.15773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T09:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"6bdd44bf0aec25ebdd59bac20325fe70f9517d65dcfe47fd1aaf73939f2e76ab","abstract_canon_sha256":"57b904fcdf2a9b344ce89138794545e4dcc62c55e9e91a8c888e2879536f1dad"},"schema_version":"1.0"},"canonical_sha256":"43ccbbd1daf0900c3fb0d51b40694ec3ee04a1f59eb711633cc597ebaee8a795","source":{"kind":"arxiv","id":"2605.15773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15773","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15773v1","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15773","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPGLXUO26CIA","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_16","alias_value":"IPGLXUO26CIAYP5Q","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_8","alias_value":"IPGLXUO2","created_at":"2026-05-20T00:01:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IPGLXUO26CIAYP5Q2UNUA2KOYP","target":"record","payload":{"canonical_record":{"source":{"id":"2605.15773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T09:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"6bdd44bf0aec25ebdd59bac20325fe70f9517d65dcfe47fd1aaf73939f2e76ab","abstract_canon_sha256":"57b904fcdf2a9b344ce89138794545e4dcc62c55e9e91a8c888e2879536f1dad"},"schema_version":"1.0"},"canonical_sha256":"43ccbbd1daf0900c3fb0d51b40694ec3ee04a1f59eb711633cc597ebaee8a795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:17.564476Z","signature_b64":"vwXLnhZBDsUASxCLSI41b1PkrCyjsJVSK9JXTwUNgup022Liy000OdxWPdfXV3pL+Vap7yFEQ519CNVExhLIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43ccbbd1daf0900c3fb0d51b40694ec3ee04a1f59eb711633cc597ebaee8a795","last_reissued_at":"2026-05-20T00:01:17.563811Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:17.563811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.15773","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":"2026-05-20T00:01:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uURq8lU1qUMCZPST+CONYzAjlfDC05cmInWRiXE+fvPh2rzZo/h8aBidUre1LszLb93uw/yVcD8CVNz8f1RzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:10.834143Z"},"content_sha256":"6bf151cfc52d6de846e08c665aeee37fad96f8ed4389424625e40e4d838ac555","schema_version":"1.0","event_id":"sha256:6bf151cfc52d6de846e08c665aeee37fad96f8ed4389424625e40e4d838ac555"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IPGLXUO26CIAYP5Q2UNUA2KOYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arc-disjoint Steiner Cycles in Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chuchu Wang, Jie Bai, Shanshan Yu, Yuefang Sun","submitted_at":"2026-05-15T09:27:57Z","abstract_excerpt":"Let $D=(V(D), A(D))$ be a digraph of order $n$ and let $S\\subseteq V(D)$ with $2\\leq |S|\\leq n$. A directed cycle $C$ of $D$ is called a directed $S$-Steiner cycle (or, an $S$-cycle for short) if $S\\subseteq V(C)$. Steiner cycles have applications in reliable designs for telecommunication and transportation networks. Two $S$-cycles are called arc-disjoint if they have no common arcs. We use $\\lambda_{S}^{c}(D)$ to denote the maximum number of pairwise arc-disjoint $S$-cycles in $D$. The directed cycle $k$-arc-connectivity of $D$ is defined as $$\\lambda_{k}^{c} (D)=\\min\\left \\{ \\lambda _{S}^{c}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15773","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/2605.15773/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.755430Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.935732Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"803aba47e127efbfa856f30ff4e301f570d20f4b8c25b5765b45192da9fb2c93"},"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":"2026-05-20T00:01:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2f9CJ/DIdx1TwAh/BS21LWGv+cPV+XNytEvikAXkG7W0g/eDgSbId9Vb1gFOqyRSQMQGCYdOi+1lA/lVky+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:10.834612Z"},"content_sha256":"bc36bc76aeccdf10d1ec0e4e92f7cc788262f9ae3d7c48b488b3d9f5569bfde9","schema_version":"1.0","event_id":"sha256:bc36bc76aeccdf10d1ec0e4e92f7cc788262f9ae3d7c48b488b3d9f5569bfde9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/bundle.json","state_url":"https://pith.science/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/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":"2026-05-28T20:44:10Z","links":{"resolver":"https://pith.science/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP","bundle":"https://pith.science/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/bundle.json","state":"https://pith.science/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPGLXUO26CIAYP5Q2UNUA2KOYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IPGLXUO26CIAYP5Q2UNUA2KOYP","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":"57b904fcdf2a9b344ce89138794545e4dcc62c55e9e91a8c888e2879536f1dad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T09:27:57Z","title_canon_sha256":"6bdd44bf0aec25ebdd59bac20325fe70f9517d65dcfe47fd1aaf73939f2e76ab"},"schema_version":"1.0","source":{"id":"2605.15773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15773","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15773v1","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15773","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPGLXUO26CIA","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_16","alias_value":"IPGLXUO26CIAYP5Q","created_at":"2026-05-20T00:01:17Z"},{"alias_kind":"pith_short_8","alias_value":"IPGLXUO2","created_at":"2026-05-20T00:01:17Z"}],"graph_snapshots":[{"event_id":"sha256:bc36bc76aeccdf10d1ec0e4e92f7cc788262f9ae3d7c48b488b3d9f5569bfde9","target":"graph","created_at":"2026-05-20T00:01:17Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.755430Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.935732Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15773/integrity.json","findings":[],"snapshot_sha256":"803aba47e127efbfa856f30ff4e301f570d20f4b8c25b5765b45192da9fb2c93","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $D=(V(D), A(D))$ be a digraph of order $n$ and let $S\\subseteq V(D)$ with $2\\leq |S|\\leq n$. A directed cycle $C$ of $D$ is called a directed $S$-Steiner cycle (or, an $S$-cycle for short) if $S\\subseteq V(C)$. Steiner cycles have applications in reliable designs for telecommunication and transportation networks. Two $S$-cycles are called arc-disjoint if they have no common arcs. We use $\\lambda_{S}^{c}(D)$ to denote the maximum number of pairwise arc-disjoint $S$-cycles in $D$. The directed cycle $k$-arc-connectivity of $D$ is defined as $$\\lambda_{k}^{c} (D)=\\min\\left \\{ \\lambda _{S}^{c}","authors_text":"Chuchu Wang, Jie Bai, Shanshan Yu, Yuefang Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T09:27:57Z","title":"Arc-disjoint Steiner Cycles in Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15773","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":"sha256:6bf151cfc52d6de846e08c665aeee37fad96f8ed4389424625e40e4d838ac555","target":"record","created_at":"2026-05-20T00:01:17Z","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":"57b904fcdf2a9b344ce89138794545e4dcc62c55e9e91a8c888e2879536f1dad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-15T09:27:57Z","title_canon_sha256":"6bdd44bf0aec25ebdd59bac20325fe70f9517d65dcfe47fd1aaf73939f2e76ab"},"schema_version":"1.0","source":{"id":"2605.15773","kind":"arxiv","version":1}},"canonical_sha256":"43ccbbd1daf0900c3fb0d51b40694ec3ee04a1f59eb711633cc597ebaee8a795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43ccbbd1daf0900c3fb0d51b40694ec3ee04a1f59eb711633cc597ebaee8a795","first_computed_at":"2026-05-20T00:01:17.563811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:17.563811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwXLnhZBDsUASxCLSI41b1PkrCyjsJVSK9JXTwUNgup022Liy000OdxWPdfXV3pL+Vap7yFEQ519CNVExhLIAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:17.564476Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf151cfc52d6de846e08c665aeee37fad96f8ed4389424625e40e4d838ac555","sha256:bc36bc76aeccdf10d1ec0e4e92f7cc788262f9ae3d7c48b488b3d9f5569bfde9"],"state_sha256":"96655f8b13fbcd214b6e887b853dead8c0cd3550d50ca9b1517883583055d860"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/414g4K2cn7xoGY535DL+OLmzPB0BRLb7E4IibqafdyDjPDvU0ZcWJD1/O2WYQ5j3DfjY4PPz07OZJArBPzpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:44:10.838692Z","bundle_sha256":"9593bb02b88a5cb5cc7df5e8fb385fc7a34e62f2d38f809e0ebda51ba358d901"}}