Pith Number

pith:37AAOZ7P

pith:2017:37AAOZ7P2MKTJLNHOD4O6KEBCP

not attested not anchored not stored refs pending

On the number of equilibria with a given number of unstable directions

Xavier Garcia

arxiv:1709.04021 v1 · 2017-09-12 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{37AAOZ7P2MKTJLNHOD4O6KEBCP}

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	2026-05-18T00:35:15.695235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfc00767efd31534ada770f8ef288113d8501525ff0e8fa872c63b2b0aded8f1

Aliases

arxiv: 1709.04021 · arxiv_version: 1709.04021v1 · doi: 10.48550/arxiv.1709.04021 · pith_short_12: 37AAOZ7P2MKT · pith_short_16: 37AAOZ7P2MKTJLNH · pith_short_8: 37AAOZ7P

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/37AAOZ7P2MKTJLNHOD4O6KEBCP \
  | 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: dfc00767efd31534ada770f8ef288113d8501525ff0e8fa872c63b2b0aded8f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79106bc478e9912abe6c7360997c42c753525ad387da80e7396bc01e90628c48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-09-12T18:59:11Z",
    "title_canon_sha256": "6676263a5992695cf6d3599bd2b3f4d0f00fce3676c6a8063a34575d6655facf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.04021",
    "kind": "arxiv",
    "version": 1
  }
}