Pith Number

pith:RHOLKBTX

pith:2011:RHOLKBTX2ZTFDK7F6R5WXJPBQR

not attested not anchored not stored refs pending

Tverberg's theorem and graph coloring

Alexander Engstr\"om, Patrik Nor\'en

arxiv:1105.1455 v4 · 2011-05-07 · math.CO · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RHOLKBTX2ZTFDK7F6R5WXJPBQR}

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	2026-05-18T03:08:04.575800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89dcb50677d66651abe5f47b6ba5e1846180a25ed52c560758ed149305effeca

Aliases

arxiv: 1105.1455 · arxiv_version: 1105.1455v4 · doi: 10.48550/arxiv.1105.1455 · pith_short_12: RHOLKBTX2ZTF · pith_short_16: RHOLKBTX2ZTFDK7F · pith_short_8: RHOLKBTX

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/RHOLKBTX2ZTFDK7F6R5WXJPBQR \
  | 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: 89dcb50677d66651abe5f47b6ba5e1846180a25ed52c560758ed149305effeca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "860c787e62df824053d83785e9b766810fb2ca4b61b4bd47fd19240dacd34115",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-07T16:11:09Z",
    "title_canon_sha256": "817294e143715666f3763ed4686dc1a511e622e57914b27ab6b439ecbf249794"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1455",
    "kind": "arxiv",
    "version": 4
  }
}