Pith Number

pith:FH2VCAAW

pith:2019:FH2VCAAWIYU4GRMHZKB5JYNTFY

not attested not anchored not stored refs pending

Min-max theory for free boundary minimal hypersurfaces II -- General Morse index bounds and applications

Martin Man-chun Li, Qiang Guang, Xin Zhou, Zhichao Wang

arxiv:1907.12064 v1 · 2019-07-28 · math.DG · math.AP · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FH2VCAAWIYU4GRMHZKB5JYNTFY}

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	2026-07-04T23:50:05.085549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29f55100164629c34587ca83d4e1b32e2c5c4fa3d08b1b6df7c366c5962fbaab

Aliases

arxiv: 1907.12064 · arxiv_version: 1907.12064v1 · doi: 10.48550/arxiv.1907.12064 · pith_short_12: FH2VCAAWIYU4 · pith_short_16: FH2VCAAWIYU4GRMH · pith_short_8: FH2VCAAW

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/FH2VCAAWIYU4GRMHZKB5JYNTFY \
  | 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: 29f55100164629c34587ca83d4e1b32e2c5c4fa3d08b1b6df7c366c5962fbaab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95e4e2f71370cc7dc710257d8a151e765069f8d89a531fd54d7c9bb32c2155c8",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-07-28T10:24:00Z",
    "title_canon_sha256": "d724245bc8387fcaf3d236690200ee58611029adb481b017c8e06c15f37ba3a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.12064",
    "kind": "arxiv",
    "version": 1
  }
}