Pith Number

pith:T3F6MQJF

pith:2010:T3F6MQJFX3WKSZZYMHAUSMKKLF

not attested not anchored not stored refs pending

Geometry of tropical moduli spaces and linkage of graphs

Lucia Caporaso

arxiv:1001.2815 v5 · 2010-01-16 · math.AG · 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{T3F6MQJFX3WKSZZYMHAUSMKKLF}

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	2026-05-18T04:08:12.741170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ecbe64125beeca9673861c149314a596dc169dabf4468663e8ab67e58f33809

Aliases

arxiv: 1001.2815 · arxiv_version: 1001.2815v5 · doi: 10.48550/arxiv.1001.2815 · pith_short_12: T3F6MQJFX3WK · pith_short_16: T3F6MQJFX3WKSZZY · pith_short_8: T3F6MQJF

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/T3F6MQJFX3WKSZZYMHAUSMKKLF \
  | 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: 9ecbe64125beeca9673861c149314a596dc169dabf4468663e8ab67e58f33809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82267227a1a6b193c9179582a6fc341e74f8202bb958225f4a3e546175bb5a14",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-01-16T11:15:21Z",
    "title_canon_sha256": "93f47beaa308ee7a8fe5ca6812d25bcd235c8cb4650c820f2e5fd8437c748894"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.2815",
    "kind": "arxiv",
    "version": 5
  }
}