Pith Number

pith:XRMB5QMA

pith:2016:XRMB5QMAWCQD4X7BCUFL3LZVVN

not attested not anchored not stored refs pending

Strictly commutative complex orientation theory

Michael J. Hopkins, Tyler Lawson

arxiv:1603.00047 v2 · 2016-02-29 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRMB5QMAWCQD4X7BCUFL3LZVVN}

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	2026-05-18T00:38:31.384177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc581ec180b0a03e5fe1150abdaf35ab5f5f53f6f375fdf7380e9193b1cba064

Aliases

arxiv: 1603.00047 · arxiv_version: 1603.00047v2 · doi: 10.48550/arxiv.1603.00047 · pith_short_12: XRMB5QMAWCQD · pith_short_16: XRMB5QMAWCQD4X7B · pith_short_8: XRMB5QMA

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/XRMB5QMAWCQD4X7BCUFL3LZVVN \
  | 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: bc581ec180b0a03e5fe1150abdaf35ab5f5f53f6f375fdf7380e9193b1cba064

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd8ca47dd3d6c7fd43a680490e2e9d9c0942d9d5cd8646ac96b058424d17a8c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-02-29T21:24:17Z",
    "title_canon_sha256": "37ebf7381860560d7604fdb258aace4bd559d1464dafe22fd70263403d51b92a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00047",
    "kind": "arxiv",
    "version": 2
  }
}