Pith Number

pith:WA5F4RVT

pith:2021:WA5F4RVTN5EF55EGZGF7EGBCAY

not attested not anchored not stored refs pending

Directed Gaussian graphical models with toric vanishing ideals

Pratik Misra, Seth Sullivant

arxiv:2105.13357 v2 · 2021-05-27 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WA5F4RVTN5EF55EGZGF7EGBCAY}

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	2026-07-05T04:46:11.159834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b03a5e46b36f485ef486c98bf21822062436bb2bcc2928d746b8d7671004e8ee

Aliases

arxiv: 2105.13357 · arxiv_version: 2105.13357v2 · doi: 10.48550/arxiv.2105.13357 · pith_short_12: WA5F4RVTN5EF · pith_short_16: WA5F4RVTN5EF55EG · pith_short_8: WA5F4RVT

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/WA5F4RVTN5EF55EGZGF7EGBCAY \
  | 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: b03a5e46b36f485ef486c98bf21822062436bb2bcc2928d746b8d7671004e8ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "983a3a3c2d87d807ecb1ba40be561c9cb373ec7b83c074f0ecb3ab4372dc55a7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2021-05-27T17:08:23Z",
    "title_canon_sha256": "0d4d66de43566fa668fc9d22b763af454f71fd0bc7a5d50aea934f3734c288fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.13357",
    "kind": "arxiv",
    "version": 2
  }
}