Pith Number

pith:NDJF3ZLY

pith:2013:NDJF3ZLYMTI4WGRZSCC5CPC5U7

not attested not anchored not stored refs pending

Tree-irreducible automorphisms of free groups

Martin Lustig

arxiv:1306.5688 v1 · 2013-06-24 · 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{NDJF3ZLYMTI4WGRZSCC5CPC5U7}

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	2026-05-18T03:20:07.263929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68d25de57864d1cb1a399085d13c5da7f1d613af0adcfecd51f2e63fd318ec2e

Aliases

arxiv: 1306.5688 · arxiv_version: 1306.5688v1 · doi: 10.48550/arxiv.1306.5688 · pith_short_12: NDJF3ZLYMTI4 · pith_short_16: NDJF3ZLYMTI4WGRZ · pith_short_8: NDJF3ZLY

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/NDJF3ZLYMTI4WGRZSCC5CPC5U7 \
  | 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: 68d25de57864d1cb1a399085d13c5da7f1d613af0adcfecd51f2e63fd318ec2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "865b0018f9eb240d77ae4633d9aeb88972eb76be47020db11ae1a85610bc8f0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-24T17:40:53Z",
    "title_canon_sha256": "8e06e28c405c2872ecc684635c11d6c952e0b3fff2c8749e3402e7b2d2fb517d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5688",
    "kind": "arxiv",
    "version": 1
  }
}