Pith Number

pith:75I7BVLK

pith:2012:75I7BVLKYSTF4JVHQ64WEEYPQL

not attested not anchored not stored refs pending

The homotopy groups of the spectrum Tmf

Johan Konter

arxiv:1212.3656 v1 · 2012-12-15 · 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{75I7BVLKYSTF4JVHQ64WEEYPQL}

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.

Cited by

1 paper in Pith

On periodic families in the stable stems of height two

Receipt and verification

First computed	2026-05-18T03:38:22.754968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff51f0d56ac4a65e26a787b962130f82d6c5bc9fb81e25ea3c8d32fc9fb3ddf9

Aliases

arxiv: 1212.3656 · arxiv_version: 1212.3656v1 · doi: 10.48550/arxiv.1212.3656 · pith_short_12: 75I7BVLKYSTF · pith_short_16: 75I7BVLKYSTF4JVH · pith_short_8: 75I7BVLK

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/75I7BVLKYSTF4JVHQ64WEEYPQL \
  | 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: ff51f0d56ac4a65e26a787b962130f82d6c5bc9fb81e25ea3c8d32fc9fb3ddf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "997cbf777cf009c0d6d7dd832ba58c8957ea45c5565a932e5cb250a8b356e7b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-12-15T04:40:04Z",
    "title_canon_sha256": "ab1007df31a70276000ae19f3d99bc55c94857ea8ded2bfc536896a8d1a97982"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3656",
    "kind": "arxiv",
    "version": 1
  }
}