Pith Number

pith:NKOWKHXQ

pith:2015:NKOWKHXQJEPUSPGNH3IWGJNGEQ

not attested not anchored not stored refs pending

Secondary characteristic classes for subgroups of automorphism groups of free groups

Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai

arxiv:1512.06365 v2 · 2015-12-20 · math.AT · math.AG · math.GR · 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{NKOWKHXQJEPUSPGNH3IWGJNGEQ}

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	2026-05-18T01:20:51.764575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a9d651ef0491f493ccd3ed16325a6242f41fa982c7b2f0a1b054c9c8f3dc0cc

Aliases

arxiv: 1512.06365 · arxiv_version: 1512.06365v2 · doi: 10.48550/arxiv.1512.06365 · pith_short_12: NKOWKHXQJEPU · pith_short_16: NKOWKHXQJEPUSPGN · pith_short_8: NKOWKHXQ

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/NKOWKHXQJEPUSPGNH3IWGJNGEQ \
  | 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: 6a9d651ef0491f493ccd3ed16325a6242f41fa982c7b2f0a1b054c9c8f3dc0cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2be358f167ff110da461b89e3f3a0d4dee8134a37953fddc2edfb646fdcb63da",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-12-20T12:33:05Z",
    "title_canon_sha256": "805a626d59b1d0acf08d77364c85dcb44d4904374cb7e04e4df1fa5991d2e38b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06365",
    "kind": "arxiv",
    "version": 2
  }
}