Pith Number

pith:M7322COG

pith:2015:M7322COGZBRO3FFWCUL6RLJ2E2

not attested not anchored not stored refs pending

Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups

Alessandro Sisto, Jason Behrstock, Mark F. Hagen

arxiv:1512.06071 v2 · 2015-12-18 · math.GR · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7322COGZBRO3FFWCUL6RLJ2E2}

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	2026-05-18T00:45:08.499899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67f7ad09c6c862ed94b61517e8ad3a2695f0c49838bf8247b0cd290385283442

Aliases

arxiv: 1512.06071 · arxiv_version: 1512.06071v2 · doi: 10.48550/arxiv.1512.06071 · pith_short_12: M7322COGZBRO · pith_short_16: M7322COGZBRO3FFW · pith_short_8: M7322COG

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/M7322COGZBRO3FFWCUL6RLJ2E2 \
  | 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: 67f7ad09c6c862ed94b61517e8ad3a2695f0c49838bf8247b0cd290385283442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d97b8f327cc1f2d2a72c02ce2f1602075453442058d4b115fafca0417cfa46e4",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-18T18:49:44Z",
    "title_canon_sha256": "95d401af0b3478905b88659f9183e315a4655ff602f3641693a406f9bf86ad1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06071",
    "kind": "arxiv",
    "version": 2
  }
}