Pith Number

pith:2KAMSF2M

pith:2015:2KAMSF2MTPSJBDEAFFNKDTDQA3

not attested not anchored not stored refs pending

A mod 2 index theorem for pin$^-$ manifolds

Weiping Zhang

arxiv:1508.02619 v1 · 2015-08-11 · math.DG · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2KAMSF2MTPSJBDEAFFNKDTDQA3}

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	2026-05-18T01:35:28.728903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d280c9174c9be4908c80295aa1cc7006e0d53948bf2fe22f5f2e7fb2f8672de7

Aliases

arxiv: 1508.02619 · arxiv_version: 1508.02619v1 · doi: 10.48550/arxiv.1508.02619 · pith_short_12: 2KAMSF2MTPSJ · pith_short_16: 2KAMSF2MTPSJBDEA · pith_short_8: 2KAMSF2M

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/2KAMSF2MTPSJBDEAFFNKDTDQA3 \
  | 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: d280c9174c9be4908c80295aa1cc7006e0d53948bf2fe22f5f2e7fb2f8672de7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d248150b7e9cc0acfbbc3742bbd184b848f108d038ec38f0775465d94841f08",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-08-11T15:00:24Z",
    "title_canon_sha256": "0ec4e40e53266decd23a0ced5af739e69410a3049e0dd2f3713256f703baf678"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02619",
    "kind": "arxiv",
    "version": 1
  }
}