Pith Number

pith:FXRTQU76

pith:2006:FXRTQU76D5FU64OW5B3JHKFN7K

not attested not anchored not stored refs pending

A Combination Theorem for Strong Relative Hyperbolicity

Lawrence Reeves, Mahan Mj

arxiv:math/0611601 v2 · 2006-11-20 · math.GT · 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{FXRTQU76D5FU64OW5B3JHKFN7K}

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	2026-05-18T02:37:59.482563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de33853fe1f4b4f71d6e87693a8adfa8c9f56a379bd402c448a2bbbe6e2ccde

Aliases

arxiv: math/0611601 · arxiv_version: math/0611601v2 · doi: 10.48550/arxiv.math/0611601 · pith_short_12: FXRTQU76D5FU · pith_short_16: FXRTQU76D5FU64OW · pith_short_8: FXRTQU76

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/FXRTQU76D5FU64OW5B3JHKFN7K \
  | 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: 2de33853fe1f4b4f71d6e87693a8adfa8c9f56a379bd402c448a2bbbe6e2ccde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b507c3b3aace31140469bfe23454b36cc650bef5392c3ca9cbad082f2fbb61b5",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2006-11-20T10:38:20Z",
    "title_canon_sha256": "77d6d764150dddb9adf3eb3ef6415e0812a905ddc073913d8e6ecdf81dc4522d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611601",
    "kind": "arxiv",
    "version": 2
  }
}