Pith Number

pith:OVPIDSTX

pith:2025:OVPIDSTXEVHU5U7SGGCSMMIG4U

not attested not anchored not stored refs pending

Existence of infinitely many homotopy classes from $\mathbb S^3$ to $\mathbb S^2$ having a minimimzing $W^{s,\frac 3s}$-harmonic map

Adam Grzela, Katarzyna Mazowiecka

arxiv:2506.05060 v1 · 2025-06-05 · 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{OVPIDSTXEVHU5U7SGGCSMMIG4U}

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	2026-07-05T11:16:41.671506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

755e81ca77254f4ed3f23185263106e535550e300e11ae5d29e21f9a3b13c868

Aliases

arxiv: 2506.05060 · arxiv_version: 2506.05060v1 · doi: 10.48550/arxiv.2506.05060 · pith_short_12: OVPIDSTXEVHU · pith_short_16: OVPIDSTXEVHU5U7S · pith_short_8: OVPIDSTX

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/OVPIDSTXEVHU5U7SGGCSMMIG4U \
  | 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: 755e81ca77254f4ed3f23185263106e535550e300e11ae5d29e21f9a3b13c868

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de6f9d8adb6beb527edb65a6ab703a59cacbf121bcde3afbc254ff9b3c5c6c88",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-05T14:03:05Z",
    "title_canon_sha256": "56bed241dc433c92db8953c831b425d1aa4b8682d35cf5721b28ddc94028cd5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05060",
    "kind": "arxiv",
    "version": 1
  }
}