Pith Number

pith:TWMR4WKR

pith:2012:TWMR4WKRV2LDC2DREV6MWSMMGS

not attested not anchored not stored refs pending

Macroscopic dimension and duality groups

Alexander Dranishnikov

arxiv:1208.0524 v1 · 2012-08-02 · math.GT · math.AT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TWMR4WKRV2LDC2DREV6MWSMMGS}

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	2026-05-18T03:49:33.923181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d991e5951ae96316871257ccb498c34a157e142a93c36c9176a9c19cdcf41ca

Aliases

arxiv: 1208.0524 · arxiv_version: 1208.0524v1 · doi: 10.48550/arxiv.1208.0524 · pith_short_12: TWMR4WKRV2LD · pith_short_16: TWMR4WKRV2LDC2DR · pith_short_8: TWMR4WKR

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/TWMR4WKRV2LDC2DREV6MWSMMGS \
  | 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: 9d991e5951ae96316871257ccb498c34a157e142a93c36c9176a9c19cdcf41ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ba4c54f97673b3c1f43c7fbeb1fd10001222b4afd172b179ff7397572f685b6",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-08-02T15:55:47Z",
    "title_canon_sha256": "6fb527b8c1955b2a146a6a47aeb89313c997b15d9f9fb04c7aac67ce032a159b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0524",
    "kind": "arxiv",
    "version": 1
  }
}