Pith Number

pith:QF45WZHF

pith:2011:QF45WZHFEJXSMUSCECZY5YNTGZ

not attested not anchored not stored refs pending

Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres

Pawe{\l} Biernat, Piotr Bizo\'n

arxiv:1101.0713 v2 · 2011-01-04 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QF45WZHFEJXSMUSCECZY5YNTGZ}

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	2026-05-18T02:04:13.478878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8179db64e5226f26524220b38ee1b33649e5621f57bc9d06f6c87e83111c4201

Aliases

arxiv: 1101.0713 · arxiv_version: 1101.0713v2 · doi: 10.48550/arxiv.1101.0713 · pith_short_12: QF45WZHFEJXS · pith_short_16: QF45WZHFEJXSMUSC · pith_short_8: QF45WZHF

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/QF45WZHFEJXSMUSCECZY5YNTGZ \
  | 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: 8179db64e5226f26524220b38ee1b33649e5621f57bc9d06f6c87e83111c4201

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da6a17de961316f7ef5fcbbc02e8d2c20d0904070e587fd84dd2e460ffb4fa56",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-01-04T12:25:16Z",
    "title_canon_sha256": "4dd0a4da5a92431ecc8d4326e5ce4fe63e8888b24582e72324152cb3ce7d2544"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0713",
    "kind": "arxiv",
    "version": 2
  }
}