Pith Number

pith:P5YBIEKX

pith:2004:P5YBIEKXAYSBMNAGSMSB46ROMD

not attested not anchored not stored refs pending

Braid groups, free groups, and the loop space of the 2-sphere

F.R. Cohen, J. Wu

arxiv:math/0409307 v1 · 2004-09-17 · math.AT · 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{P5YBIEKXAYSBMNAGSMSB46ROMD}

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	2026-07-04T14:39:04.669584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f70141157062416340693241e7a2e60fcf605c4dea98c2b5297e97a170ed595

Aliases

arxiv: math/0409307 · arxiv_version: math/0409307v1 · doi: 10.48550/arxiv.math/0409307 · pith_short_12: P5YBIEKXAYSB · pith_short_16: P5YBIEKXAYSBMNAG · pith_short_8: P5YBIEKX

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/P5YBIEKXAYSBMNAGSMSB46ROMD \
  | 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: 7f70141157062416340693241e7a2e60fcf605c4dea98c2b5297e97a170ed595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2cf2f2df2809e36cc5500b03aa0caae2e1b2430c2e1d473b8cf8865a7f3a27f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2004-09-17T17:25:41Z",
    "title_canon_sha256": "ad27cfb2b7f58f7fb201f6be4dd7db8268d09ab589177a03df900118c78badd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409307",
    "kind": "arxiv",
    "version": 1
  }
}