Pith Number

pith:ZR4GTT2G

pith:2016:ZR4GTT2GIKGT6K4KBTEWDOPVPT

not attested not anchored not stored refs pending

Parametrized cobordism categories and the Dwyer-Weiss-Williams index theorem

George Raptis, Wolfgang Steimle

arxiv:1606.07925 v2 · 2016-06-25 · math.AT · 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{ZR4GTT2GIKGT6K4KBTEWDOPVPT}

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	2026-05-18T00:42:02.725841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc7869cf46428d3f2b8a0cc961b9f57cce82e507f85bf181fdaa03b9a733f0ef

Aliases

arxiv: 1606.07925 · arxiv_version: 1606.07925v2 · doi: 10.48550/arxiv.1606.07925 · pith_short_12: ZR4GTT2GIKGT · pith_short_16: ZR4GTT2GIKGT6K4K · pith_short_8: ZR4GTT2G

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/ZR4GTT2GIKGT6K4KBTEWDOPVPT \
  | 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: cc7869cf46428d3f2b8a0cc961b9f57cce82e507f85bf181fdaa03b9a733f0ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4c8323b6ca8981f736e96d3bc9fdb34437c329778307d503fd33041355fa513",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-06-25T16:03:04Z",
    "title_canon_sha256": "334f15bb3ea7fce507813eddb65df103dc3a49f86767c0fc892324047ec2cb92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07925",
    "kind": "arxiv",
    "version": 2
  }
}