Pith Number

pith:4DI2XC5W

pith:2015:4DI2XC5WT6HCOVO7WLUAAPOQ6X

not attested not anchored not stored refs pending

Homological stability of $Aut(F_n)$ revisited

Mladen Bestvina

arxiv:1508.03876 v1 · 2015-08-16 · 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{4DI2XC5WT6HCOVO7WLUAAPOQ6X}

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	2026-05-18T01:35:14.996527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0d1ab8bb69f8e2755dfb2e8003dd0f5e81f7f7b68c766e7c8fec3454aa29b60

Aliases

arxiv: 1508.03876 · arxiv_version: 1508.03876v1 · doi: 10.48550/arxiv.1508.03876 · pith_short_12: 4DI2XC5WT6HC · pith_short_16: 4DI2XC5WT6HCOVO7 · pith_short_8: 4DI2XC5W

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/4DI2XC5WT6HCOVO7WLUAAPOQ6X \
  | 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: e0d1ab8bb69f8e2755dfb2e8003dd0f5e81f7f7b68c766e7c8fec3454aa29b60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35951b9f23e320d7c7b06ba70f6a2acf9276842ecc21df292e692983fa2e4404",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-08-16T22:10:22Z",
    "title_canon_sha256": "f68d7ecf8cb2721a78a01a461549b24ca43595658c240e52989bc2212790789d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03876",
    "kind": "arxiv",
    "version": 1
  }
}