Pith Number

pith:5KPWM52L

pith:2026:5KPWM52LGOOKFWBAFJLGJW67X4

not attested not anchored not stored refs pending

Existence of Yamabe stability optimizers

Jesse Ratzkin, Jo\~ao Henrique Andrade, Juncheng Wei, Tobias K\"onig

arxiv:2608.10324 v1 · 2026-08-10 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5KPWM52LGOOKFWBAFJLGJW67X4}

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	2026-08-12T00:23:52.711499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea9f66774b339ca2d8202a5664dbdfbf3019a803e095a45e48f0f45ef3f39dbb

Aliases

arxiv: 2608.10324 · arxiv_version: 2608.10324v1 · doi: 10.48550/arxiv.2608.10324 · pith_short_12: 5KPWM52LGOOK · pith_short_16: 5KPWM52LGOOKFWBA · pith_short_8: 5KPWM52L

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/5KPWM52LGOOKFWBAFJLGJW67X4 \
  | 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: ea9f66774b339ca2d8202a5664dbdfbf3019a803e095a45e48f0f45ef3f39dbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae801680645189ac75470ceae50bd9572ea185ee3da084b093b1fb53a3a25539",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-08-10T23:49:20Z",
    "title_canon_sha256": "ae0c4d53d422e00102e19d2ca754074c0a028938e4008daaeab6eaf41e21e1ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.10324",
    "kind": "arxiv",
    "version": 1
  }
}