Pith Number

pith:YJ4JYCAJ

pith:2019:YJ4JYCAJNMOHGIPUK6IVCPBU6J

not attested not anchored not stored refs pending

Local behaviour of the gradient flow of an analytic function near the unstable set of a critical point

Graeme Wilkin

arxiv:1904.08045 v1 · 2019-04-17 · math.CA · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YJ4JYCAJNMOHGIPUK6IVCPBU6J}

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	2026-05-17T23:48:18.952745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2789c08096b1c7321f45791513c34f278d4a170a5be232b2057f97e10097335

Aliases

arxiv: 1904.08045 · arxiv_version: 1904.08045v1 · doi: 10.48550/arxiv.1904.08045 · pith_short_12: YJ4JYCAJNMOH · pith_short_16: YJ4JYCAJNMOHGIPU · pith_short_8: YJ4JYCAJ

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/YJ4JYCAJNMOHGIPUK6IVCPBU6J \
  | 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: c2789c08096b1c7321f45791513c34f278d4a170a5be232b2057f97e10097335

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bb0da6d6f8c00cb7cf844148f701f59a8bfc2f8f3cb5f02cc426c904e9c3dd8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-04-17T01:48:59Z",
    "title_canon_sha256": "163581c0ba3c4748277dd93560471b164c5750a15713db743f0b12e2e103f216"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.08045",
    "kind": "arxiv",
    "version": 1
  }
}