{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MPRF4JC7KQJZWRU6OUXU7ML335","short_pith_number":"pith:MPRF4JC7","canonical_record":{"source":{"id":"1608.01278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T18:26:34Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cfe37cbc3ea213b6bc950e91be1cf466909697274d509b0e503a8f0976710386","abstract_canon_sha256":"c11a7f1fb9dfd8a885cd49da44513f6c65d65d02e51952adda1dc82d53e5e01f"},"schema_version":"1.0"},"canonical_sha256":"63e25e245f54139b469e752f4fb17bdf70b37119a8d9cbe26aa5cb21196f80d8","source":{"kind":"arxiv","id":"1608.01278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01278","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01278v1","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01278","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"MPRF4JC7KQJZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPRF4JC7KQJZWRU6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPRF4JC7","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MPRF4JC7KQJZWRU6OUXU7ML335","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T18:26:34Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cfe37cbc3ea213b6bc950e91be1cf466909697274d509b0e503a8f0976710386","abstract_canon_sha256":"c11a7f1fb9dfd8a885cd49da44513f6c65d65d02e51952adda1dc82d53e5e01f"},"schema_version":"1.0"},"canonical_sha256":"63e25e245f54139b469e752f4fb17bdf70b37119a8d9cbe26aa5cb21196f80d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:55.989802Z","signature_b64":"sSwuvfxAJ6lg/I+rLWkZ7D3GwpG+BCEolxh31pjWHzmQQUNpWGrsnPMLJFnidJhYx8H+zS1EORPzaCsHiFAPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63e25e245f54139b469e752f4fb17bdf70b37119a8d9cbe26aa5cb21196f80d8","last_reissued_at":"2026-05-18T01:09:55.989175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:55.989175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01278","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":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDbUj5ADeJxDhigyRyzfaCs2pc+2ESOHO2d/YoCibrsqGdf33++Wz8M8J1SIqjoebB0ImqhR5WQv6eIBjPdsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:12:32.125141Z"},"content_sha256":"de167810c4e0aee018e86fac5b2e3be4d8bc3fdb88a0ee2046cc3564770ef032","schema_version":"1.0","event_id":"sha256:de167810c4e0aee018e86fac5b2e3be4d8bc3fdb88a0ee2046cc3564770ef032"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MPRF4JC7KQJZWRU6OUXU7ML335","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Packing Loose Hamilton Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Asaf Ferber, Daniel Montealegre, Kyle Luh, Oanh Nguyen","submitted_at":"2016-08-03T18:26:34Z","abstract_excerpt":"A subset $C$ of edges in a $k$-uniform hypergraph $H$ is a \\emph{loose Hamilton cycle} if $C$ covers all the vertices of $H$ and there exists a cyclic ordering of these vertices such that the edges in $C$ are segments of that order and such that every two consecutive edges share exactly one vertex. The binomial random $k$-uniform hypergraph $H^k_{n,p}$ has vertex set $[n]$ and an edge set $E$ obtained by adding each $k$-tuple $e\\in \\binom{[n]}{k}$ to $E$ with probability $p$, independently at random.\n  Here we consider the problem of finding edge-disjoint loose Hamilton cycles covering all but"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01278","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":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0SgyvBDyupb8U/q/GPeVHt4ZSVCkcP6X3ljbcW8JeUeYWf6vFXCEA6XC8rnsi108/qDOrSKNwHiZyggKRoiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:12:32.125547Z"},"content_sha256":"991adba82cabf3d0a43e4ea48e252cb0dd0ab7324eb1b5e9df7ae2eacd821693","schema_version":"1.0","event_id":"sha256:991adba82cabf3d0a43e4ea48e252cb0dd0ab7324eb1b5e9df7ae2eacd821693"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPRF4JC7KQJZWRU6OUXU7ML335/bundle.json","state_url":"https://pith.science/pith/MPRF4JC7KQJZWRU6OUXU7ML335/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPRF4JC7KQJZWRU6OUXU7ML335/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":"2026-05-30T07:12:32Z","links":{"resolver":"https://pith.science/pith/MPRF4JC7KQJZWRU6OUXU7ML335","bundle":"https://pith.science/pith/MPRF4JC7KQJZWRU6OUXU7ML335/bundle.json","state":"https://pith.science/pith/MPRF4JC7KQJZWRU6OUXU7ML335/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPRF4JC7KQJZWRU6OUXU7ML335/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MPRF4JC7KQJZWRU6OUXU7ML335","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":"c11a7f1fb9dfd8a885cd49da44513f6c65d65d02e51952adda1dc82d53e5e01f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T18:26:34Z","title_canon_sha256":"cfe37cbc3ea213b6bc950e91be1cf466909697274d509b0e503a8f0976710386"},"schema_version":"1.0","source":{"id":"1608.01278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01278","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01278v1","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01278","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"MPRF4JC7KQJZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPRF4JC7KQJZWRU6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPRF4JC7","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:991adba82cabf3d0a43e4ea48e252cb0dd0ab7324eb1b5e9df7ae2eacd821693","target":"graph","created_at":"2026-05-18T01:09:55Z","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":"A subset $C$ of edges in a $k$-uniform hypergraph $H$ is a \\emph{loose Hamilton cycle} if $C$ covers all the vertices of $H$ and there exists a cyclic ordering of these vertices such that the edges in $C$ are segments of that order and such that every two consecutive edges share exactly one vertex. The binomial random $k$-uniform hypergraph $H^k_{n,p}$ has vertex set $[n]$ and an edge set $E$ obtained by adding each $k$-tuple $e\\in \\binom{[n]}{k}$ to $E$ with probability $p$, independently at random.\n  Here we consider the problem of finding edge-disjoint loose Hamilton cycles covering all but","authors_text":"Asaf Ferber, Daniel Montealegre, Kyle Luh, Oanh Nguyen","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T18:26:34Z","title":"Packing Loose Hamilton Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01278","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:de167810c4e0aee018e86fac5b2e3be4d8bc3fdb88a0ee2046cc3564770ef032","target":"record","created_at":"2026-05-18T01:09:55Z","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":"c11a7f1fb9dfd8a885cd49da44513f6c65d65d02e51952adda1dc82d53e5e01f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-03T18:26:34Z","title_canon_sha256":"cfe37cbc3ea213b6bc950e91be1cf466909697274d509b0e503a8f0976710386"},"schema_version":"1.0","source":{"id":"1608.01278","kind":"arxiv","version":1}},"canonical_sha256":"63e25e245f54139b469e752f4fb17bdf70b37119a8d9cbe26aa5cb21196f80d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63e25e245f54139b469e752f4fb17bdf70b37119a8d9cbe26aa5cb21196f80d8","first_computed_at":"2026-05-18T01:09:55.989175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:55.989175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sSwuvfxAJ6lg/I+rLWkZ7D3GwpG+BCEolxh31pjWHzmQQUNpWGrsnPMLJFnidJhYx8H+zS1EORPzaCsHiFAPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:55.989802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de167810c4e0aee018e86fac5b2e3be4d8bc3fdb88a0ee2046cc3564770ef032","sha256:991adba82cabf3d0a43e4ea48e252cb0dd0ab7324eb1b5e9df7ae2eacd821693"],"state_sha256":"0f56b452d13fecc81080be3b04436c19c018deda73661802fb0a33d2d6026562"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wh6sxIqNT/i9nAmtdIJ4WtIiPPQMLlucTAVldYZlQexjFNXNPZ+Y9fWIp5HsOkboQJE7jPjec0xcsIQnGpWxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:12:32.128004Z","bundle_sha256":"c97d073b836b09a39890576f50abc7397f134dbf00b33ab10ea2b2c903fce35a"}}