Pith Number

pith:FUPKRIAK

pith:2011:FUPKRIAKU4LV3OKVAY6OOX5HNQ

not attested not anchored not stored refs pending

Min-type Morse theory for configuration spaces of hard spheres

Matthew Kahle, Peter Bubenik, Yuliy Baryshnikov

arxiv:1108.3061 v2 · 2011-08-15 · math.AT · cs.RO · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FUPKRIAKU4LV3OKVAY6OOX5HNQ}

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	2026-05-18T02:52:13.023333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d1ea8a00aa7175db955063ce75fa76c1d8e156df67fcc4701f7e877b49ef695

Aliases

arxiv: 1108.3061 · arxiv_version: 1108.3061v2 · doi: 10.48550/arxiv.1108.3061 · pith_short_12: FUPKRIAKU4LV · pith_short_16: FUPKRIAKU4LV3OKV · pith_short_8: FUPKRIAK

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/FUPKRIAKU4LV3OKVAY6OOX5HNQ \
  | 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: 2d1ea8a00aa7175db955063ce75fa76c1d8e156df67fcc4701f7e877b49ef695

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "620e5e8493b3d01cce36a68b4786c5bfe7e73dd789670a5f255daa764c21e8bc",
    "cross_cats_sorted": [
      "cs.RO",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-08-15T19:12:24Z",
    "title_canon_sha256": "394cad8a5cf1aa4d6f915d45f8ca35ff424b43dd0b6c03ec6da03b8d4382fb75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3061",
    "kind": "arxiv",
    "version": 2
  }
}