Pith Number

pith:Z7WSZSKO

pith:2025:Z7WSZSKOM5NJDWDLLFRQDCU2T4

not attested not anchored not stored refs pending

Multiple Blow-Up Phenomena for $Q$-Curvature in High Dimensions

Almir Silva Santos, Rayssa Caju

arxiv:2512.13811 v2 · 2025-12-15 · 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{Z7WSZSKOM5NJDWDLLFRQDCU2T4}

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	2026-06-25T01:18:36.240748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfed2cc94e675a91d86b5963018a9a9f0268dbf1be2f7fd8f283348bba1cc94f

Aliases

arxiv: 2512.13811 · arxiv_version: 2512.13811v2 · doi: 10.48550/arxiv.2512.13811 · pith_short_12: Z7WSZSKOM5NJ · pith_short_16: Z7WSZSKOM5NJDWDL · pith_short_8: Z7WSZSKO

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/Z7WSZSKOM5NJDWDLLFRQDCU2T4 \
  | 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: cfed2cc94e675a91d86b5963018a9a9f0268dbf1be2f7fd8f283348bba1cc94f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8626ccf1c6a915d1864b68264f48e2463d4a692bd564597129720f6308343764",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-12-15T19:00:58Z",
    "title_canon_sha256": "13d49029f151dd6a9822f36bad9ff696e66f338cbf7779f82e9b0dbc02e1c83d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.13811",
    "kind": "arxiv",
    "version": 2
  }
}