{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RL7MUGKQUONTB5YSOU2VXFOB35","short_pith_number":"pith:RL7MUGKQ","canonical_record":{"source":{"id":"1610.09093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-28T06:42:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"472a92b88fb5b1174b976a70771d9f3c112ede8fba6129cbbe05113989232c61","abstract_canon_sha256":"3773efc947d2028a47d21011175e3a8b7c4e3b1e7efe37b9da58922635ba34c5"},"schema_version":"1.0"},"canonical_sha256":"8afeca1950a39b30f71275355b95c1df60fbdb87e5e436885d7f7765d761fb4b","source":{"kind":"arxiv","id":"1610.09093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09093","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09093v1","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09093","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"RL7MUGKQUONT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RL7MUGKQUONTB5YS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RL7MUGKQ","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RL7MUGKQUONTB5YSOU2VXFOB35","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-28T06:42:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"472a92b88fb5b1174b976a70771d9f3c112ede8fba6129cbbe05113989232c61","abstract_canon_sha256":"3773efc947d2028a47d21011175e3a8b7c4e3b1e7efe37b9da58922635ba34c5"},"schema_version":"1.0"},"canonical_sha256":"8afeca1950a39b30f71275355b95c1df60fbdb87e5e436885d7f7765d761fb4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:59.166335Z","signature_b64":"OkekdAB8j49MPEpBbsFEMF3zjvYi2AODHLOo4GwbYxl6ImryShCGWtPpNDCRAnHU2ZrzNRe+j+gxM7w2SM6LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8afeca1950a39b30f71275355b95c1df60fbdb87e5e436885d7f7765d761fb4b","last_reissued_at":"2026-05-18T01:00:59.165751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:59.165751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09093","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":"2026-05-18T01:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUXDuLsGx9G52jj2jRtbyvsqgVmcqZ8vLSC8qtZMBb0eActLpix2uJpAx7GBxPjusO/HuNBotcR8tu7EFxcaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:39:35.159905Z"},"content_sha256":"1b797592b84b4357f1a4c50f1dc7e8d5292c8ef4ed43f2ebe01a9aa72d50990e","schema_version":"1.0","event_id":"sha256:1b797592b84b4357f1a4c50f1dc7e8d5292c8ef4ed43f2ebe01a9aa72d50990e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RL7MUGKQUONTB5YSOU2VXFOB35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More on foxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jens M. Schmidt, Matthias Kriesell","submitted_at":"2016-10-28T06:42:43Z","abstract_excerpt":"An edge in a $k$-connected graph $G$ is called {\\em $k$-contractible} if the graph $G/e$ obtained from $G$ by contracting $e$ is $k$-connected. Generalizing earlier results on $3$-contractible edges in spanning trees of $3$-connected graphs, we prove that (except for the graphs $K_{k+1}$ if $k \\in \\{1,2\\}$) (a) every spanning tree of a $k$-connected triangle free graph has two $k$-contractible edges, (b) every spanning tree of a $k$-connected graph of minimum degree at least $\\frac{3}{2}k-1$ has two $k$-contractible edges, (c) for $k>3$, every DFS tree of a $k$-connected graph of minimum degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09093","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":"2026-05-18T01:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jzV0Gwo/cWtvHqTvzNdDJVwZf+5Ag4o3fSowAwDxpJNFi9i5UjhPc7sktwkbK7STPTj9FBaxGp8WDUHPGwACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:39:35.160484Z"},"content_sha256":"d006220548be75984e0e36b5f8557ade04190b8ca339c46397e1f481ff41ffba","schema_version":"1.0","event_id":"sha256:d006220548be75984e0e36b5f8557ade04190b8ca339c46397e1f481ff41ffba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RL7MUGKQUONTB5YSOU2VXFOB35/bundle.json","state_url":"https://pith.science/pith/RL7MUGKQUONTB5YSOU2VXFOB35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RL7MUGKQUONTB5YSOU2VXFOB35/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":"2026-06-22T10:39:35Z","links":{"resolver":"https://pith.science/pith/RL7MUGKQUONTB5YSOU2VXFOB35","bundle":"https://pith.science/pith/RL7MUGKQUONTB5YSOU2VXFOB35/bundle.json","state":"https://pith.science/pith/RL7MUGKQUONTB5YSOU2VXFOB35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RL7MUGKQUONTB5YSOU2VXFOB35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RL7MUGKQUONTB5YSOU2VXFOB35","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":"3773efc947d2028a47d21011175e3a8b7c4e3b1e7efe37b9da58922635ba34c5","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-28T06:42:43Z","title_canon_sha256":"472a92b88fb5b1174b976a70771d9f3c112ede8fba6129cbbe05113989232c61"},"schema_version":"1.0","source":{"id":"1610.09093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09093","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09093v1","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09093","created_at":"2026-05-18T01:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"RL7MUGKQUONT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RL7MUGKQUONTB5YS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RL7MUGKQ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:d006220548be75984e0e36b5f8557ade04190b8ca339c46397e1f481ff41ffba","target":"graph","created_at":"2026-05-18T01:00:59Z","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":"An edge in a $k$-connected graph $G$ is called {\\em $k$-contractible} if the graph $G/e$ obtained from $G$ by contracting $e$ is $k$-connected. Generalizing earlier results on $3$-contractible edges in spanning trees of $3$-connected graphs, we prove that (except for the graphs $K_{k+1}$ if $k \\in \\{1,2\\}$) (a) every spanning tree of a $k$-connected triangle free graph has two $k$-contractible edges, (b) every spanning tree of a $k$-connected graph of minimum degree at least $\\frac{3}{2}k-1$ has two $k$-contractible edges, (c) for $k>3$, every DFS tree of a $k$-connected graph of minimum degre","authors_text":"Jens M. Schmidt, Matthias Kriesell","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-28T06:42:43Z","title":"More on foxes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09093","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":"sha256:1b797592b84b4357f1a4c50f1dc7e8d5292c8ef4ed43f2ebe01a9aa72d50990e","target":"record","created_at":"2026-05-18T01:00:59Z","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":"3773efc947d2028a47d21011175e3a8b7c4e3b1e7efe37b9da58922635ba34c5","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-28T06:42:43Z","title_canon_sha256":"472a92b88fb5b1174b976a70771d9f3c112ede8fba6129cbbe05113989232c61"},"schema_version":"1.0","source":{"id":"1610.09093","kind":"arxiv","version":1}},"canonical_sha256":"8afeca1950a39b30f71275355b95c1df60fbdb87e5e436885d7f7765d761fb4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8afeca1950a39b30f71275355b95c1df60fbdb87e5e436885d7f7765d761fb4b","first_computed_at":"2026-05-18T01:00:59.165751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:59.165751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkekdAB8j49MPEpBbsFEMF3zjvYi2AODHLOo4GwbYxl6ImryShCGWtPpNDCRAnHU2ZrzNRe+j+gxM7w2SM6LAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:59.166335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b797592b84b4357f1a4c50f1dc7e8d5292c8ef4ed43f2ebe01a9aa72d50990e","sha256:d006220548be75984e0e36b5f8557ade04190b8ca339c46397e1f481ff41ffba"],"state_sha256":"f1f96fc6bff560064fc539eb81d8feb7b126b3571e3b96000658a1d836c2cf8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cf2YOhk4PI3ZiCCcKKfVhf6Z2RUktd6MuWkaBNvwpFDzmtZD44pnElTBOhtLqEFkyIZAzlcZtIj7/aMBM5D/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:39:35.163131Z","bundle_sha256":"b72abed02b8571aee3ce8f0521889e6de661b16d0b01d001a0db47a417d6a9a8"}}