Pith Number

pith:PZXSVQIH

pith:2015:PZXSVQIHHHKDX4YGIRMV3GGYYL

not attested not anchored not stored refs pending

Existence of minimal surfaces of arbitrary large Morse index

Haozhao Li, Xin Zhou

arxiv:1504.00970 v2 · 2015-04-04 · 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{PZXSVQIHHHKDX4YGIRMV3GGYYL}

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	2026-05-18T01:14:09.148846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e6f2ac10739d43bf30644595d98d8c2e80989e8e16eabe9ec917755b7049d22

Aliases

arxiv: 1504.00970 · arxiv_version: 1504.00970v2 · doi: 10.48550/arxiv.1504.00970 · pith_short_12: PZXSVQIHHHKD · pith_short_16: PZXSVQIHHHKDX4YG · pith_short_8: PZXSVQIH

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/PZXSVQIHHHKDX4YGIRMV3GGYYL \
  | 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: 7e6f2ac10739d43bf30644595d98d8c2e80989e8e16eabe9ec917755b7049d22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "236124e9e718f90aa68f7655398e5fc2427dd5b03b59d3d8608575272ee65666",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-04-04T02:16:14Z",
    "title_canon_sha256": "6635159758a25e72072d15fe781bc785d6079c1ee6d74e4e2133ae04e2d6f540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00970",
    "kind": "arxiv",
    "version": 2
  }
}