{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XHNJ62NYLWRJ62VJUQUWKNOICV","short_pith_number":"pith:XHNJ62NY","schema_version":"1.0","canonical_sha256":"b9da9f69b85da29f6aa9a4296535c8156026f54ad815095fd1e385fee97777ee","source":{"kind":"arxiv","id":"1512.06145","version":2},"attestation_state":"computed","paper":{"title":"Long paths in first passage percolation on the complete graph II. Global branching dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. R. Nardi, J. Goodman, M. Eckhoff, R. van der Hofstad","submitted_at":"2015-12-18T21:31:58Z","abstract_excerpt":"We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [6]. We describe our results in terms of a sequence of parameters $(s_n)_{n\\geq 1}$ that quantifies the extreme-value behavior of small weights, and that describes different universality classes for first passage percolation on the complete graph. We consider both $n$-independent as well as $n$-dependent edge weights. The simplest example consists of edge weights of the form $E^{s_n}$,"},"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":"1512.06145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-18T21:31:58Z","cross_cats_sorted":[],"title_canon_sha256":"9f365ce3368e4aef5ddadffbfa794114b7ac87e053533db8a3367d6068d92d4a","abstract_canon_sha256":"5d876346781ef10f19dce588653a82e4d92adde84693d1a1397e1ee8321a7ea7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:53.678155Z","signature_b64":"A3f1aPROZSRlxsKdpyrKYSsHjJYPldKZKEimac1OvkxgZoh7ZMZbSMYPyLZo61AGGH7yScFJDS6A6xeaYno8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9da9f69b85da29f6aa9a4296535c8156026f54ad815095fd1e385fee97777ee","last_reissued_at":"2026-05-18T01:23:53.677574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:53.677574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long paths in first passage percolation on the complete graph II. Global branching dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. R. Nardi, J. Goodman, M. Eckhoff, R. van der Hofstad","submitted_at":"2015-12-18T21:31:58Z","abstract_excerpt":"We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [6]. We describe our results in terms of a sequence of parameters $(s_n)_{n\\geq 1}$ that quantifies the extreme-value behavior of small weights, and that describes different universality classes for first passage percolation on the complete graph. We consider both $n$-independent as well as $n$-dependent edge weights. The simplest example consists of edge weights of the form $E^{s_n}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06145","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.06145","created_at":"2026-05-18T01:23:53.677673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06145v2","created_at":"2026-05-18T01:23:53.677673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06145","created_at":"2026-05-18T01:23:53.677673+00:00"},{"alias_kind":"pith_short_12","alias_value":"XHNJ62NYLWRJ","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XHNJ62NYLWRJ62VJ","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XHNJ62NY","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV","json":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV.json","graph_json":"https://pith.science/api/pith-number/XHNJ62NYLWRJ62VJUQUWKNOICV/graph.json","events_json":"https://pith.science/api/pith-number/XHNJ62NYLWRJ62VJUQUWKNOICV/events.json","paper":"https://pith.science/paper/XHNJ62NY"},"agent_actions":{"view_html":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV","download_json":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV.json","view_paper":"https://pith.science/paper/XHNJ62NY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06145&json=true","fetch_graph":"https://pith.science/api/pith-number/XHNJ62NYLWRJ62VJUQUWKNOICV/graph.json","fetch_events":"https://pith.science/api/pith-number/XHNJ62NYLWRJ62VJUQUWKNOICV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV/action/storage_attestation","attest_author":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV/action/author_attestation","sign_citation":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV/action/citation_signature","submit_replication":"https://pith.science/pith/XHNJ62NYLWRJ62VJUQUWKNOICV/action/replication_record"}},"created_at":"2026-05-18T01:23:53.677673+00:00","updated_at":"2026-05-18T01:23:53.677673+00:00"}