Pith Number

pith:2HAB5RGM

pith:2006:2HAB5RGMPGZA36NBOSICL5R2ZO

not attested not anchored not stored refs pending

Abelian subgroups of \Out(F_n)

Mark Feighn, Michael Handel

arxiv:math/0612705 v1 · 2006-12-22 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HAB5RGMPGZA36NBOSICL5R2ZO}

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	2026-05-18T02:37:59.431986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1c01ec4cc79b20df9a1749025f63acb9b3c36a8c197fcd9f9b6f50f2e2d64cb

Aliases

arxiv: math/0612705 · arxiv_version: math/0612705v1 · doi: 10.48550/arxiv.math/0612705 · pith_short_12: 2HAB5RGMPGZA · pith_short_16: 2HAB5RGMPGZA36NB · pith_short_8: 2HAB5RGM

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/2HAB5RGMPGZA36NBOSICL5R2ZO \
  | 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: d1c01ec4cc79b20df9a1749025f63acb9b3c36a8c197fcd9f9b6f50f2e2d64cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b36d1131722b5f552b7a6723b425357ee92f0b4b32fd6b3dd6ad829606d6594d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-12-22T14:09:09Z",
    "title_canon_sha256": "9ca43c95ca08a04a686e75fb215eeda74aba53050150158f86b7a2e7738fa678"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612705",
    "kind": "arxiv",
    "version": 1
  }
}