Pith Number

pith:LMDMJJBJ

pith:2015:LMDMJJBJXPRYAK5VRX5BWXNOCI

not attested not anchored not stored refs pending

Random extensions of free groups and surface groups are hyperbolic

Giulio Tiozzo, Samuel J. Taylor

arxiv:1501.02846 v1 · 2015-01-12 · math.GT · math.DS · 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{LMDMJJBJXPRYAK5VRX5BWXNOCI}

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	2026-05-18T02:29:31.097197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b06c4a429bbe3802bb58dfa1b5dae12184f76ce629364deaa4d4ff9bee91fba

Aliases

arxiv: 1501.02846 · arxiv_version: 1501.02846v1 · doi: 10.48550/arxiv.1501.02846 · pith_short_12: LMDMJJBJXPRY · pith_short_16: LMDMJJBJXPRYAK5V · pith_short_8: LMDMJJBJ

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/LMDMJJBJXPRYAK5VRX5BWXNOCI \
  | 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: 5b06c4a429bbe3802bb58dfa1b5dae12184f76ce629364deaa4d4ff9bee91fba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acbebd99604716fb17bc9f33b869e064b6a7ad1911fe62c24d325bde15924aa5",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-01-12T23:04:22Z",
    "title_canon_sha256": "6aeb6146b3a2446cd467b0483f5d456a8fbf5a2b6755d681ad98c1a28f18dccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.02846",
    "kind": "arxiv",
    "version": 1
  }
}