Pith Number

pith:USUOWQLZ

pith:2008:USUOWQLZX4KBJKCFWKDJCFIUHR

not attested not anchored not stored refs pending

A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networks

Abraham D. Flaxman, David B. Wilson, Omer Angel

arxiv:0810.4908 v2 · 2008-10-27 · math.PR · cond-mat.stat-mech · math.CO

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

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	2026-05-18T03:54:06.391782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4a8eb4179bf1414a845b2869115143c5721d18ddb5befb117a7e84df2401133

Aliases

arxiv: 0810.4908 · arxiv_version: 0810.4908v2 · doi: 10.48550/arxiv.0810.4908 · pith_short_12: USUOWQLZX4KB · pith_short_16: USUOWQLZX4KBJKCF · pith_short_8: USUOWQLZ

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/USUOWQLZX4KBJKCFWKDJCFIUHR \
  | 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: a4a8eb4179bf1414a845b2869115143c5721d18ddb5befb117a7e84df2401133

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f03c19597be6aa098207c07e34052c116e08d64a579c245ad880d2c8666b9d6",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-10-27T19:15:31Z",
    "title_canon_sha256": "9b4cb4d4e08a9844d77fe55a746b3a2119770458e76e70c4682cc4afe772df94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4908",
    "kind": "arxiv",
    "version": 2
  }
}