Pith Number

pith:QQYH6VPW

pith:2013:QQYH6VPWCVQQBFC3V6SJLFKHAE

not attested not anchored not stored refs pending

Convergent sequences of sparse graphs: A large deviations approach

Christian Borgs, David Gamarnik, Jennifer Chayes

arxiv:1302.4615 v1 · 2013-02-19 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQYH6VPWCVQQBFC3V6SJLFKHAE}

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	2026-05-18T03:33:12.737074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84307f55f6156100945bafa4959547013dd3dbf7439c41707cf33bbbdff4a4d5

Aliases

arxiv: 1302.4615 · arxiv_version: 1302.4615v1 · doi: 10.48550/arxiv.1302.4615 · pith_short_12: QQYH6VPWCVQQ · pith_short_16: QQYH6VPWCVQQBFC3 · pith_short_8: QQYH6VPW

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/QQYH6VPWCVQQBFC3V6SJLFKHAE \
  | 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: 84307f55f6156100945bafa4959547013dd3dbf7439c41707cf33bbbdff4a4d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a725ffc06c04a58670451f6ec2c0ed8fecfa62bc1dc67fe50fe43d19d5fc1f7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-19T14:16:46Z",
    "title_canon_sha256": "65b2d78759c15a970c11a1169aed46557236da7580aa71177f600bd0c89745fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4615",
    "kind": "arxiv",
    "version": 1
  }
}