{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4XUA4SLIL7MW2R6DHIAGAFG344","short_pith_number":"pith:4XUA4SLI","canonical_record":{"source":{"id":"1603.04180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-14T09:53:01Z","cross_cats_sorted":[],"title_canon_sha256":"73457520c6e7bb0a8947816e755baee01cd2be4fde17aa5c33df4dbfd86bd219","abstract_canon_sha256":"4ea06cdd736258f0375532a946d51f11442f978aa8bae99e36243b4664c4c4fd"},"schema_version":"1.0"},"canonical_sha256":"e5e80e49685fd96d47c33a006014dbe713518d47f4957745c5b369e546ef8d8a","source":{"kind":"arxiv","id":"1603.04180","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04180","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04180v2","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04180","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"4XUA4SLIL7MW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4XUA4SLIL7MW2R6D","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4XUA4SLI","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4XUA4SLIL7MW2R6DHIAGAFG344","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-14T09:53:01Z","cross_cats_sorted":[],"title_canon_sha256":"73457520c6e7bb0a8947816e755baee01cd2be4fde17aa5c33df4dbfd86bd219","abstract_canon_sha256":"4ea06cdd736258f0375532a946d51f11442f978aa8bae99e36243b4664c4c4fd"},"schema_version":"1.0"},"canonical_sha256":"e5e80e49685fd96d47c33a006014dbe713518d47f4957745c5b369e546ef8d8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:45.457008Z","signature_b64":"BU0PwfcG7+5XVN/D0Px1geaXE8J0gwn72Tj5N507JN5TxfI1YVFjJibRX/hYdM9WVVWlknv8I59y/YXkOyjVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e80e49685fd96d47c33a006014dbe713518d47f4957745c5b369e546ef8d8a","last_reissued_at":"2026-05-18T00:31:45.456311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:45.456311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04180","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6yIAAr8nbpdrN1ao+FcGhPyOEBWDj22rXRngRLx89DcVW2qh4RsiRtmS6wcj0HlA6U04kzC/8uzjy9f0Srs/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:30:59.558569Z"},"content_sha256":"091ae9fba2b95444051bb856660cbbb5b1a643950bf3c0631a91d7fc73d10328","schema_version":"1.0","event_id":"sha256:091ae9fba2b95444051bb856660cbbb5b1a643950bf3c0631a91d7fc73d10328"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4XUA4SLIL7MW2R6DHIAGAFG344","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fabian Schulenburg, Guilherme Oliveira Mota, Jakob Schnitzer, Josefran de Oliveira Bastos, Mathias Schacht","submitted_at":"2016-03-14T09:53:01Z","abstract_excerpt":"We prove that for all $k\\geq 4$ and $1\\leq\\ell<k/2$, every $k$-uniform hypergraph $\\mathcal{H}$ on $n$ vertices with $\\delta_{k-2}(\\mathcal{H})\\geq\\left(\\frac{4(k-\\ell)-1}{4(k-\\ell)^2}+o(1)\\right)\\binom{n}{2}$ contains a Hamiltonian $\\ell$-cycle if $k-\\ell$ divides $n$. This degree condition is asymptotically best possible. The case $k=3$ was addressed earlier by Bu{\\ss} et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04180","kind":"arxiv","version":2},"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":"2026-05-18T00:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNZEtOGAGOdfKd406fhZ5BBDNHOrxNWjFVQdVgcvceDGW/+thGN5gkOVib6/X0z+DB66WaSi4zFVZYXfFqTtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:30:59.559234Z"},"content_sha256":"eebb4e5b5ead1e7b36926434bf5bc8fabd388f379fc156190d6088dda79f61fc","schema_version":"1.0","event_id":"sha256:eebb4e5b5ead1e7b36926434bf5bc8fabd388f379fc156190d6088dda79f61fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XUA4SLIL7MW2R6DHIAGAFG344/bundle.json","state_url":"https://pith.science/pith/4XUA4SLIL7MW2R6DHIAGAFG344/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XUA4SLIL7MW2R6DHIAGAFG344/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":"2026-05-27T03:30:59Z","links":{"resolver":"https://pith.science/pith/4XUA4SLIL7MW2R6DHIAGAFG344","bundle":"https://pith.science/pith/4XUA4SLIL7MW2R6DHIAGAFG344/bundle.json","state":"https://pith.science/pith/4XUA4SLIL7MW2R6DHIAGAFG344/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XUA4SLIL7MW2R6DHIAGAFG344/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4XUA4SLIL7MW2R6DHIAGAFG344","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":"4ea06cdd736258f0375532a946d51f11442f978aa8bae99e36243b4664c4c4fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-14T09:53:01Z","title_canon_sha256":"73457520c6e7bb0a8947816e755baee01cd2be4fde17aa5c33df4dbfd86bd219"},"schema_version":"1.0","source":{"id":"1603.04180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04180","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04180v2","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04180","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"4XUA4SLIL7MW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4XUA4SLIL7MW2R6D","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4XUA4SLI","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:eebb4e5b5ead1e7b36926434bf5bc8fabd388f379fc156190d6088dda79f61fc","target":"graph","created_at":"2026-05-18T00:31:45Z","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":"We prove that for all $k\\geq 4$ and $1\\leq\\ell<k/2$, every $k$-uniform hypergraph $\\mathcal{H}$ on $n$ vertices with $\\delta_{k-2}(\\mathcal{H})\\geq\\left(\\frac{4(k-\\ell)-1}{4(k-\\ell)^2}+o(1)\\right)\\binom{n}{2}$ contains a Hamiltonian $\\ell$-cycle if $k-\\ell$ divides $n$. This degree condition is asymptotically best possible. The case $k=3$ was addressed earlier by Bu{\\ss} et al.","authors_text":"Fabian Schulenburg, Guilherme Oliveira Mota, Jakob Schnitzer, Josefran de Oliveira Bastos, Mathias Schacht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-14T09:53:01Z","title":"Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04180","kind":"arxiv","version":2},"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":"sha256:091ae9fba2b95444051bb856660cbbb5b1a643950bf3c0631a91d7fc73d10328","target":"record","created_at":"2026-05-18T00:31:45Z","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":"4ea06cdd736258f0375532a946d51f11442f978aa8bae99e36243b4664c4c4fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-14T09:53:01Z","title_canon_sha256":"73457520c6e7bb0a8947816e755baee01cd2be4fde17aa5c33df4dbfd86bd219"},"schema_version":"1.0","source":{"id":"1603.04180","kind":"arxiv","version":2}},"canonical_sha256":"e5e80e49685fd96d47c33a006014dbe713518d47f4957745c5b369e546ef8d8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e80e49685fd96d47c33a006014dbe713518d47f4957745c5b369e546ef8d8a","first_computed_at":"2026-05-18T00:31:45.456311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:45.456311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BU0PwfcG7+5XVN/D0Px1geaXE8J0gwn72Tj5N507JN5TxfI1YVFjJibRX/hYdM9WVVWlknv8I59y/YXkOyjVCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:45.457008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091ae9fba2b95444051bb856660cbbb5b1a643950bf3c0631a91d7fc73d10328","sha256:eebb4e5b5ead1e7b36926434bf5bc8fabd388f379fc156190d6088dda79f61fc"],"state_sha256":"af6869a32d7ba4a43ab452572dcc6a693c0e5743462d125f17b79b001c3afc23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhuX9xJzdCr3lxXWyysFlQCABvmkCZfI5DsLsstTgk+AiqVFxqZk1x4PUppUohjjqcZLLjnpzQb6Y7Zz2qfRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:30:59.562687Z","bundle_sha256":"2902d8d49e1eb02cef2d6a0eb59d7cc439152dc810d62a734cd0221523b6cf25"}}