Pith Number

pith:TQ7XNP6S

pith:2009:TQ7XNP6SWAHDTMNY47XBX7J3DM

not attested not anchored not stored refs pending

Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics

Balazs Rath

arxiv:0912.3904 v5 · 2009-12-19 · 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{TQ7XNP6SWAHDTMNY47XBX7J3DM}

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	2026-05-18T03:57:01.038084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c

Aliases

arxiv: 0912.3904 · arxiv_version: 0912.3904v5 · doi: 10.48550/arxiv.0912.3904 · pith_short_12: TQ7XNP6SWAHD · pith_short_16: TQ7XNP6SWAHDTMNY · pith_short_8: TQ7XNP6S

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/TQ7XNP6SWAHDTMNY47XBX7J3DM \
  | 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: 9c3f76bfd2b00e39b1b8e7ee1bfd3b1b18013bd639786138c3296027b9154f1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b23c6f391d9069b71ad95e42214e2240c6c5052706083236e943303ac4d70bea",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-19T16:13:32Z",
    "title_canon_sha256": "1bf01f8b1d8eb332b0714a990644d7265a2cc88b728478a17045509e99d72ea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3904",
    "kind": "arxiv",
    "version": 5
  }
}