Pith Number

pith:3FJVXJFP

pith:2018:3FJVXJFPOSVI6CATVQU7K6GHJS

not attested not anchored not stored refs pending

The biharmonic homotopy problem for unit vector fields on 2-tori

E. Loubeau, M. Markellos

arxiv:1804.11169 v1 · 2018-04-30 · 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{3FJVXJFPOSVI6CATVQU7K6GHJS}

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	2026-05-18T00:17:14.423402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9535ba4af74aa8f0813ac29f578c74ca1d71cc0acca46772b5c4e2932ff626b

Aliases

arxiv: 1804.11169 · arxiv_version: 1804.11169v1 · doi: 10.48550/arxiv.1804.11169 · pith_short_12: 3FJVXJFPOSVI · pith_short_16: 3FJVXJFPOSVI6CAT · pith_short_8: 3FJVXJFP

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/3FJVXJFPOSVI6CATVQU7K6GHJS \
  | 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: d9535ba4af74aa8f0813ac29f578c74ca1d71cc0acca46772b5c4e2932ff626b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d2648174765918c3ea9e2f95118830c1668c6b649a4510beb60b92499e0eb34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-04-30T13:06:04Z",
    "title_canon_sha256": "d3f143b6383d810f369b9ee620c4a1187dd693c81e750e1d7f5c9e726c6acc4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.11169",
    "kind": "arxiv",
    "version": 1
  }
}