Pith Number

pith:WMHMVIK2

pith:2015:WMHMVIK2DGAW774CGGD4D4WEV6

not attested not anchored not stored refs pending

Hierarchically hyperbolic spaces II: Combination theorems and the distance formula

Alessandro Sisto, Jason Behrstock, Mark F. Hagen

arxiv:1509.00632 v4 · 2015-09-02 · 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{WMHMVIK2DGAW774CGGD4D4WEV6}

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	2026-05-17T23:44:15.780874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b30ecaa15a19816fff823187c1f2c4af88bc76d2dd54bd9be84f00c826a8042a

Aliases

arxiv: 1509.00632 · arxiv_version: 1509.00632v4 · doi: 10.48550/arxiv.1509.00632 · pith_short_12: WMHMVIK2DGAW · pith_short_16: WMHMVIK2DGAW774C · pith_short_8: WMHMVIK2

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/WMHMVIK2DGAW774CGGD4D4WEV6 \
  | 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: b30ecaa15a19816fff823187c1f2c4af88bc76d2dd54bd9be84f00c826a8042a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58eb39ba3b98c310371650718499caeb5f67a9c93100d7dbe9734c0c57fc114e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-02T10:34:37Z",
    "title_canon_sha256": "7b8ab67248a2c0b9b05d2a3ebc181b7bdea8c706077613629377b2165b8acb7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00632",
    "kind": "arxiv",
    "version": 4
  }
}