Pith Number

pith:MBXXIZXG

pith:2017:MBXXIZXGQEFTOT74PJXJAKVIN2

not attested not anchored not stored refs pending

Morse Theory and Relative Equilibria in the Planar $n$-Vortex Problem

Gareth E. Roberts

arxiv:1709.01242 v1 · 2017-09-05 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MBXXIZXGQEFTOT74PJXJAKVIN2}

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	2026-05-17T23:52:08.397947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

606f7466e6810b374ffc7a6e902aa86ebf168a8fe998840ccb3752c0db0e4d55

Aliases

arxiv: 1709.01242 · arxiv_version: 1709.01242v1 · doi: 10.48550/arxiv.1709.01242 · pith_short_12: MBXXIZXGQEFT · pith_short_16: MBXXIZXGQEFTOT74 · pith_short_8: MBXXIZXG

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/MBXXIZXGQEFTOT74PJXJAKVIN2 \
  | 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: 606f7466e6810b374ffc7a6e902aa86ebf168a8fe998840ccb3752c0db0e4d55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "466a67b9b8161fbea6ef6df78293cfc04dca8e7b759443a0d18c4bd91423ecaf",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-09-05T05:55:14Z",
    "title_canon_sha256": "a1c70a398ee03c6872197686b71051b392c029ba602b956fc13424d854528c78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.01242",
    "kind": "arxiv",
    "version": 1
  }
}