Pith Number

pith:I3OY7B7H

pith:2021:I3OY7B7HRNB4QDTTFA52HUDS2L

not attested not anchored not stored refs pending

Rooted tree graphs and the Butcher group: Combinatorics of elementary perturbation theory

William G. Faris

arxiv:2101.09364 v1 · 2021-01-22 · 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{I3OY7B7HRNB4QDTTFA52HUDS2L}

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.

Cited by

1 paper in Pith

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis

Receipt and verification

First computed	2026-07-05T02:26:55.040629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46dd8f87e78b43c80e73283ba3d072d2ee649b4a732f511c1f1a7d48e77aa7e1

Aliases

arxiv: 2101.09364 · arxiv_version: 2101.09364v1 · doi: 10.48550/arxiv.2101.09364 · pith_short_12: I3OY7B7HRNB4 · pith_short_16: I3OY7B7HRNB4QDTT · pith_short_8: I3OY7B7H

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/I3OY7B7HRNB4QDTTFA52HUDS2L \
  | 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: 46dd8f87e78b43c80e73283ba3d072d2ee649b4a732f511c1f1a7d48e77aa7e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a8cdf43a4342574ddaabe20a43e9876dfe76264b7f03d27589f83ef4a1e73de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-01-22T22:18:56Z",
    "title_canon_sha256": "66b0b693f8ab8ea5f48545e4e3c34cce7e385c3459c655dcd6f329855caf20b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.09364",
    "kind": "arxiv",
    "version": 1
  }
}