Pith Number

pith:GUKX45ZF

pith:2021:GUKX45ZFICV6R5FXXIBZ4PKPJW

not attested not anchored not stored refs pending

Thick embeddings of graphs into symmetric spaces via coarse geometry

Benjamin Barrett, David Hume, Elia Portnoy, Larry Guth

arxiv:2112.05305 v3 · 2021-12-10 · math.GT · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUKX45ZFICV6R5FXXIBZ4PKPJW}

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

Almost planar finitely presented groups

Receipt and verification

First computed	2026-07-05T07:22:59.485741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35157e772540abe8f4b7ba039e3d4f4da9726f3792fcd21c4d62d91e2316e2fe

Aliases

arxiv: 2112.05305 · arxiv_version: 2112.05305v3 · doi: 10.48550/arxiv.2112.05305 · pith_short_12: GUKX45ZFICV6 · pith_short_16: GUKX45ZFICV6R5FX · pith_short_8: GUKX45ZF

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/GUKX45ZFICV6R5FXXIBZ4PKPJW \
  | 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: 35157e772540abe8f4b7ba039e3d4f4da9726f3792fcd21c4d62d91e2316e2fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5535d19d7f5a866a3fbbfac836e257941d271188b29bfbeedf2c83454c35323a",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-12-10T02:53:51Z",
    "title_canon_sha256": "6233871c9bb8d615dd84eb29f22e0378e92ff1586405bb395f300f7d94914f57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05305",
    "kind": "arxiv",
    "version": 3
  }
}