Pith Number

pith:5U3FELEQ

pith:2006:5U3FELEQ3DFH53UCGNKJT7QFYG

not attested not anchored not stored refs pending

The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

Takuya Sakasai

arxiv:math/0601314 v2 · 2006-01-13 · 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{5U3FELEQ3DFH53UCGNKJT7QFYG}

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	2026-05-17T23:47:21.437483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed36522c90d8ca7eee82335499fe05c1909f1f8d8ccd4d14938d7a8825bf3a49

Aliases

arxiv: math/0601314 · arxiv_version: math/0601314v2 · doi: 10.48550/arxiv.math/0601314 · pith_short_12: 5U3FELEQ3DFH · pith_short_16: 5U3FELEQ3DFH53UC · pith_short_8: 5U3FELEQ

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/5U3FELEQ3DFH53UCGNKJT7QFYG \
  | 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: ed36522c90d8ca7eee82335499fe05c1909f1f8d8ccd4d14938d7a8825bf3a49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24fc8acdc2b1401e64a72a04e9a82a6e763d58ab7c8f99801a8c8120e7111433",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2006-01-13T14:04:04Z",
    "title_canon_sha256": "89846f60b56c009f85e6d3c473b1227009a0f9c3c94caf900ba31abf4f83926e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601314",
    "kind": "arxiv",
    "version": 2
  }
}