Pith Number

pith:MMQYHX4T

pith:2008:MMQYHX4TNZ47VP3G57WOFUUEKY

not attested not anchored not stored refs pending

Proof of the Caratheodory Conjecture

Brendan Guilfoyle, Wilhelm Klingenberg

arxiv:0808.0851 v4 · 2008-08-06 · math.DG · math.AP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMQYHX4TNZ47VP3G57WOFUUEKY}

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

Cuspidal Singularities in Collapsing Domain Walls

Receipt and verification

First computed	2026-07-05T10:01:58.285276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

632183df936e79fabf66efece2d284563a00181e2a3f1d228f7226cbc625a7c3

Aliases

arxiv: 0808.0851 · arxiv_version: 0808.0851v4 · doi: 10.48550/arxiv.0808.0851 · pith_short_12: MMQYHX4TNZ47 · pith_short_16: MMQYHX4TNZ47VP3G · pith_short_8: MMQYHX4T

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/MMQYHX4TNZ47VP3G57WOFUUEKY \
  | 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: 632183df936e79fabf66efece2d284563a00181e2a3f1d228f7226cbc625a7c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ffc4483ab7f883610d1eb33be1a0ba9fb9f6994ad9e15571d88f522af42a369",
    "cross_cats_sorted": [
      "math.AP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2008-08-06T15:03:20Z",
    "title_canon_sha256": "6a9bcdb3626b6a5da9216cf22ffffb7cd1e346be3c25b351ca9f1ce9cdbad2a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.0851",
    "kind": "arxiv",
    "version": 4
  }
}