Pith Number

pith:52QFGCDB

pith:2016:52QFGCDBQDZXTGDSZBJ4YT6FMH

not attested not anchored not stored refs pending

The geometric Hopf invariant and surgery theory

Andrew Ranicki, Michael Crabb

arxiv:1602.08832 v2 · 2016-02-29 · 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{52QFGCDBQDZXTGDSZBJ4YT6FMH}

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	2026-05-18T00:33:37.096727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea053086180f3799872c853cc4fc561e5b3e7c811b60355b9ec5dadf0342714

Aliases

arxiv: 1602.08832 · arxiv_version: 1602.08832v2 · doi: 10.48550/arxiv.1602.08832 · pith_short_12: 52QFGCDBQDZX · pith_short_16: 52QFGCDBQDZXTGDS · pith_short_8: 52QFGCDB

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/52QFGCDBQDZXTGDSZBJ4YT6FMH \
  | 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: eea053086180f3799872c853cc4fc561e5b3e7c811b60355b9ec5dadf0342714

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f35b4851e0c8867f4e234633c94ab614c87af6101ba76f58d85dcf663ccd2714",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-02-29T05:52:07Z",
    "title_canon_sha256": "2ab72c0fa6d9c2897e8b9069ceb8cb7f29846b3e92af302761c379f0ab7ac7bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08832",
    "kind": "arxiv",
    "version": 2
  }
}