Pith Number

pith:PPM55GSD

pith:2026:PPM55GSDHUDOIUPOJYU4ZPXCRO

not attested not anchored not stored refs pending

Collapsing-tube type II blow-up for the energy-supercritical heat equation

Juncheng Wei, Manuel del Pino, Monica Musso, Yifu Zhou

arxiv:2607.16733 v1 · 2026-07-18 · 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{PPM55GSDHUDOIUPOJYU4ZPXCRO}

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	2026-07-21T01:20:24.114373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bd9de9a433d06e451ee4e29ccbee28ba060a4016f09bb2b3f6070a85d43b431

Aliases

arxiv: 2607.16733 · arxiv_version: 2607.16733v1 · doi: 10.48550/arxiv.2607.16733 · pith_short_12: PPM55GSDHUDO · pith_short_16: PPM55GSDHUDOIUPO · pith_short_8: PPM55GSD

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/PPM55GSDHUDOIUPOJYU4ZPXCRO \
  | 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: 7bd9de9a433d06e451ee4e29ccbee28ba060a4016f09bb2b3f6070a85d43b431

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ab09ac7b5db05cf255a797ff98c088871a3b950ea7b02db21cad08ae2909e6e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-18T09:47:07Z",
    "title_canon_sha256": "28bd8deeec2204b3fe17566ca4df8cbea8a50e966d5eebe4086144eebca56ede"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16733",
    "kind": "arxiv",
    "version": 1
  }
}