Pith Number

pith:U5UNCAS5

pith:2018:U5UNCAS5OJXBVGJW5POHEPPW62

not attested not anchored not stored refs pending

Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant

Jianfeng Lin, Michael J. Hopkins, XiaoLin Danny Shi, Zhouli Xu

arxiv:1812.04052 v3 · 2018-12-10 · math.AT · math.DG · 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{U5UNCAS5OJXBVGJW5POHEPPW62}

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	2026-05-17T23:55:18.844529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a768d1025d726e1a9936ebdc723df6f69e81b6a05d30ed806371dd7fe03e50d6

Aliases

arxiv: 1812.04052 · arxiv_version: 1812.04052v3 · doi: 10.48550/arxiv.1812.04052 · pith_short_12: U5UNCAS5OJXB · pith_short_16: U5UNCAS5OJXBVGJW · pith_short_8: U5UNCAS5

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/U5UNCAS5OJXBVGJW5POHEPPW62 \
  | 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: a768d1025d726e1a9936ebdc723df6f69e81b6a05d30ed806371dd7fe03e50d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abe16d258d18efe988bc5ecbcca04cc88d2e48788bc6c99f54ae85ccc833de2a",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-12-10T19:39:51Z",
    "title_canon_sha256": "9879fd05a6da5a2ce9d67299877d39d473db4957fe070234a2bc80bf1069af90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04052",
    "kind": "arxiv",
    "version": 3
  }
}