Pith Number

pith:TTDYI4XW

pith:2011:TTDYI4XWHY4SWRTEQYYXFMJWZU

not attested not anchored not stored refs pending

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii

arxiv:1112.6097 v3 · 2011-12-28 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTDYI4XWHY4SWRTEQYYXFMJWZU}

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	2026-05-18T03:58:36.675372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cc78472f63e392b4664863172b136cd3c74d04d00a82154e563720222b8145a

Aliases

arxiv: 1112.6097 · arxiv_version: 1112.6097v3 · doi: 10.48550/arxiv.1112.6097 · pith_short_12: TTDYI4XWHY4S · pith_short_16: TTDYI4XWHY4SWRTE · pith_short_8: TTDYI4XW

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/TTDYI4XWHY4SWRTEQYYXFMJWZU \
  | 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: 9cc78472f63e392b4664863172b136cd3c74d04d00a82154e563720222b8145a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c57d2f8245bd8bf2be1b04731cc12b921acca6bec36c82cfea902c300f11f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-28T11:07:39Z",
    "title_canon_sha256": "d6ccefc0451849b675cbe27b51dcd4e8392aeaec5170eba0d8cc6afedc2c76f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6097",
    "kind": "arxiv",
    "version": 3
  }
}