Pith Number

pith:NMR5OOY5

pith:2026:NMR5OOY5DMYK5A2ZOIXP5VPR5B

not attested not anchored not stored refs pending

Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime

Cheng Mao, Hang Du, Jiaming Xu, Nike Sun, Yihong Wu

arxiv:2607.02013 v1 · 2026-07-02 · math.PR · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NMR5OOY5DMYK5A2ZOIXP5VPR5B}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-03T01:17:37.050414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b23d73b1d1b30ae8359722efed5f1e86966100957e18569f56e3ff9c2e8a0cd

Aliases

arxiv: 2607.02013 · arxiv_version: 2607.02013v1 · doi: 10.48550/arxiv.2607.02013 · pith_short_12: NMR5OOY5DMYK · pith_short_16: NMR5OOY5DMYK5A2Z · pith_short_8: NMR5OOY5

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NMR5OOY5DMYK5A2ZOIXP5VPR5B \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6b23d73b1d1b30ae8359722efed5f1e86966100957e18569f56e3ff9c2e8a0cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3eac8c071efef2407a10a7c9ee2952cd632410b74d76cb1729791a73574f09c",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-02T10:45:46Z",
    "title_canon_sha256": "477cd5760a53a195d50071f29858fb65427c5147445385f038fcd1ce4199cfba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02013",
    "kind": "arxiv",
    "version": 1
  }
}