Pith Number

pith:M52XYFO4

pith:2012:M52XYFO4HQPQIIWKIP36DKSLFJ

not attested not anchored not stored refs pending

The associated family of an elliptic surface and applications to minimal submanifolds

Marcos Dajczer, Theodoros Vlachos

arxiv:1212.1974 v3 · 2012-12-10 · 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{M52XYFO4HQPQIIWKIP36DKSLFJ}

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	2026-05-18T02:27:06.003165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67757c15dc3c1f0422ca43f7e1aa4b2a431758be94e5be7829e15410a5ec7c73

Aliases

arxiv: 1212.1974 · arxiv_version: 1212.1974v3 · doi: 10.48550/arxiv.1212.1974 · pith_short_12: M52XYFO4HQPQ · pith_short_16: M52XYFO4HQPQIIWK · pith_short_8: M52XYFO4

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/M52XYFO4HQPQIIWKIP36DKSLFJ \
  | 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: 67757c15dc3c1f0422ca43f7e1aa4b2a431758be94e5be7829e15410a5ec7c73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1822d048d202ad5564939256ce3c243ef72c306f60415962db4d66619e6077c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-12-10T06:06:23Z",
    "title_canon_sha256": "dfce1a637e91b00a1c8cd611c2022f08ade0b08316dce81d98544587b0803744"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1974",
    "kind": "arxiv",
    "version": 3
  }
}