Pith Number

pith:JFUR5TE2

pith:2012:JFUR5TE2IRTBUMNZSD7N33WBC2

not attested not anchored not stored refs pending

Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2

Niko Naumann, Tyler Lawson

arxiv:1203.1696 v2 · 2012-03-08 · 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{JFUR5TE2IRTBUMNZSD7N33WBC2}

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	2026-05-18T03:36:26.969844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49691ecc9a44661a31b990feddeec116a387a99e43cb0a23bf3ff61f2105b510

Aliases

arxiv: 1203.1696 · arxiv_version: 1203.1696v2 · doi: 10.48550/arxiv.1203.1696 · pith_short_12: JFUR5TE2IRTB · pith_short_16: JFUR5TE2IRTBUMNZ · pith_short_8: JFUR5TE2

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/JFUR5TE2IRTBUMNZSD7N33WBC2 \
  | 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: 49691ecc9a44661a31b990feddeec116a387a99e43cb0a23bf3ff61f2105b510

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5229b9cc91d851bf92ea2952be8c6b24df724d6f7471e1fbdbdd42ec20726ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-03-08T06:01:13Z",
    "title_canon_sha256": "ac25174c8108c3ee0406f3c75f24b54cf086d722c8489814c0f8c7f737cae62b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1696",
    "kind": "arxiv",
    "version": 2
  }
}