Pith Number

pith:VMGAWQOO

pith:2012:VMGAWQOOES3JSTWVEQSQW5EHQP

not attested not anchored not stored refs pending

The power operation structure on Morava E-theory of height 2 at the prime 3

Yifei Zhu

arxiv:1210.3730 v1 · 2012-10-13 · 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{VMGAWQOOES3JSTWVEQSQW5EHQP}

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	2026-05-18T02:41:42.875747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab0c0b41ce24b6994ed524250b748783eca3d79e548093beb00ea06335c22bd4

Aliases

arxiv: 1210.3730 · arxiv_version: 1210.3730v1 · doi: 10.48550/arxiv.1210.3730 · pith_short_12: VMGAWQOOES3J · pith_short_16: VMGAWQOOES3JSTWV · pith_short_8: VMGAWQOO

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/VMGAWQOOES3JSTWVEQSQW5EHQP \
  | 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: ab0c0b41ce24b6994ed524250b748783eca3d79e548093beb00ea06335c22bd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9ce0676e1e8fb299aef4dda5c212c27e42a034bc209f59a88819fcd59307098",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-10-13T18:10:25Z",
    "title_canon_sha256": "21c8729eacea2e36bdc1e2c44c1e80f1b5b9bf811d432b2102d62cd32f824829"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3730",
    "kind": "arxiv",
    "version": 1
  }
}