Pith Number

pith:W5FJJEN4

pith:2016:W5FJJEN42XCAEENV7BRODNRLR3

not attested not anchored not stored refs pending

Boundaries and automorphisms of hierarchically hyperbolic spaces

Alessandro Sisto, Mark F. Hagen, Matthew G. Durham

arxiv:1604.01061 v3 · 2016-04-04 · math.GT · math.GR · 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{W5FJJEN42XCAEENV7BRODNRLR3}

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	2026-05-18T00:20:59.639038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b74a9491bcd5c40211b5f862e1b62b8ee59f6d2736b688f239dcfea49aab1d4e

Aliases

arxiv: 1604.01061 · arxiv_version: 1604.01061v3 · doi: 10.48550/arxiv.1604.01061 · pith_short_12: W5FJJEN42XCA · pith_short_16: W5FJJEN42XCAEENV · pith_short_8: W5FJJEN4

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/W5FJJEN42XCAEENV7BRODNRLR3 \
  | 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: b74a9491bcd5c40211b5f862e1b62b8ee59f6d2736b688f239dcfea49aab1d4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de8c17b01a1f7a592258c8ea99619e46b863ff631ea37068fef8e99687b3f0f2",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-04-04T21:01:23Z",
    "title_canon_sha256": "e216bc86495e5859492e31a672bccfd1d83dc66fa8a87e30099fbe91a6c72ae4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.01061",
    "kind": "arxiv",
    "version": 3
  }
}