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A classical result in the theory of random graphs asserts that for $G \\sim \\mathbb{G}(n,p)$, asymptotically almost surely the necessary condition $\\delta(G) \\geq 2$ is also sufficient to ensure Hamiltonicity. Resolving a problem of Christoph, Nenadov, and Petrova, we augment this result by proving that for $G \\sim \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.19731","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-24T15:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"fce3bc260b094f84986c3a5d0d3f0ab3b8e2066ad7c68193f71398c1f0f1bebf","abstract_canon_sha256":"4bdef8feabe2df6b0b886346fde0401a70a3fc2f97c35d110c31d76cf1e072d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:31.947474Z","signature_b64":"UAeSYr4yfcG1cC296gi7IaNIOoocDtrJ6s8hBztiMlz/7o5A6jaIGT7DSDdBl3Yc3YONm40g2/ecJ8Es4FMPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9776c761d09eecaed028b3286cb55acac526cc231fc32c78b0e3c67686b20516","last_reissued_at":"2026-07-05T11:32:31.946990Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:31.946990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hamilton cycle space of random graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hefetz, Michael Krivelevich","submitted_at":"2025-06-24T15:49:24Z","abstract_excerpt":"The cycle space of a graph $G$, denoted $C(G)$, is a vector space over ${\\mathbb F}_2$, spanned by all incidence vectors of edge-sets of cycles of $G$. 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Resolving a problem of Christoph, Nenadov, and Petrova, we augment this result by proving that for $G \\sim \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19731","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.19731/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.19731","created_at":"2026-07-05T11:32:31.947045+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.19731v2","created_at":"2026-07-05T11:32:31.947045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19731","created_at":"2026-07-05T11:32:31.947045+00:00"},{"alias_kind":"pith_short_12","alias_value":"S53MOYOQT3WK","created_at":"2026-07-05T11:32:31.947045+00:00"},{"alias_kind":"pith_short_16","alias_value":"S53MOYOQT3WK5UBI","created_at":"2026-07-05T11:32:31.947045+00:00"},{"alias_kind":"pith_short_8","alias_value":"S53MOYOQ","created_at":"2026-07-05T11:32:31.947045+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05835","citing_title":"On graphs whose cycle space is spanned by their Hamilton cycles","ref_index":19,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL","json":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL.json","graph_json":"https://pith.science/api/pith-number/S53MOYOQT3WK5UBIWMUGZNK2ZL/graph.json","events_json":"https://pith.science/api/pith-number/S53MOYOQT3WK5UBIWMUGZNK2ZL/events.json","paper":"https://pith.science/paper/S53MOYOQ"},"agent_actions":{"view_html":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL","download_json":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL.json","view_paper":"https://pith.science/paper/S53MOYOQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.19731&json=true","fetch_graph":"https://pith.science/api/pith-number/S53MOYOQT3WK5UBIWMUGZNK2ZL/graph.json","fetch_events":"https://pith.science/api/pith-number/S53MOYOQT3WK5UBIWMUGZNK2ZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL/action/storage_attestation","attest_author":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL/action/author_attestation","sign_citation":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL/action/citation_signature","submit_replication":"https://pith.science/pith/S53MOYOQT3WK5UBIWMUGZNK2ZL/action/replication_record"}},"created_at":"2026-07-05T11:32:31.947045+00:00","updated_at":"2026-07-05T11:32:31.947045+00:00"}