Pith Number

pith:5UN26B5Y

pith:2026:5UN26B5YKCMEAACSGAAHLSJSKL

not attested not anchored not stored refs pending

Sharp Phase Transition for Ellipsoid Fitting

Aaron Potechin, Jeff Xu, Madhur Tulsiani, Sofia de la Cerda

arxiv:2608.12415 v1 · 2026-08-12 · 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{5UN26B5YKCMEAACSGAAHLSJSKL}

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	2026-08-14T00:42:48.685453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed1baf07b85098400052300075c93252c8e3a69dfe8d5ec9c8f1857b88d6fd4e

Aliases

arxiv: 2608.12415 · arxiv_version: 2608.12415v1 · doi: 10.48550/arxiv.2608.12415 · pith_short_12: 5UN26B5YKCME · pith_short_16: 5UN26B5YKCMEAACS · pith_short_8: 5UN26B5Y

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/5UN26B5YKCMEAACSGAAHLSJSKL \
  | 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: ed1baf07b85098400052300075c93252c8e3a69dfe8d5ec9c8f1857b88d6fd4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba1b605ec928ff1a83b6a8540d52e7e494d8506441539a41212e97dc9a49a819",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-12T04:09:06Z",
    "title_canon_sha256": "dbb21da7650a09d58d66e8b2fd93f47c2dbc0979eb408df071302b1cfca218e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12415",
    "kind": "arxiv",
    "version": 1
  }
}