Pith Number

pith:YUHFUN3M

pith:2006:YUHFUN3MAEG2AQS67RR7NWOOW7

not attested not anchored not stored refs pending

Convex projective structures on Gromov--Thurston manifolds

Michael Kapovich

arxiv:math/0604231 v2 · 2006-04-11 · math.DG · math.GR · 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{YUHFUN3MAEG2AQS67RR7NWOOW7}

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	2026-05-18T02:37:59.629877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c50e5a376c010da0425efc63f6d9ceb7e4f06167c2ed6e6ba9fa6f9b1e33a302

Aliases

arxiv: math/0604231 · arxiv_version: math/0604231v2 · doi: 10.48550/arxiv.math/0604231 · pith_short_12: YUHFUN3MAEG2 · pith_short_16: YUHFUN3MAEG2AQS6 · pith_short_8: YUHFUN3M

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/YUHFUN3MAEG2AQS67RR7NWOOW7 \
  | 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: c50e5a376c010da0425efc63f6d9ceb7e4f06167c2ed6e6ba9fa6f9b1e33a302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf86739952326ecc4fcfb703955d1e604659b7cd7c5c0793312f0a531a4b1b05",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2006-04-11T01:33:58Z",
    "title_canon_sha256": "02ed8cb1c9c3d47c2858336a41921b1db13035e0922a0ec495039ee4d21e7ff1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0604231",
    "kind": "arxiv",
    "version": 2
  }
}