Pith Number

pith:E25UYBBR

pith:2017:E25UYBBRCM75XBSVIAZ6EHC6VC

not attested not anchored not stored refs pending

On geodesic ray bundles in hyperbolic groups

Nicholas Touikan

arxiv:1706.01979 v1 · 2017-06-06 · 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{E25UYBBRCM75XBSVIAZ6EHC6VC}

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	2026-05-18T00:12:06.356526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26bb4c0431133fdb86554033e21c5ea8af6b61bd540b37949da549499f59c71b

Aliases

arxiv: 1706.01979 · arxiv_version: 1706.01979v1 · doi: 10.48550/arxiv.1706.01979 · pith_short_12: E25UYBBRCM75 · pith_short_16: E25UYBBRCM75XBSV · pith_short_8: E25UYBBR

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/E25UYBBRCM75XBSVIAZ6EHC6VC \
  | 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: 26bb4c0431133fdb86554033e21c5ea8af6b61bd540b37949da549499f59c71b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c22812eefd8f14e7f0ca6c2c63fe29c1aa33243ca963fb751ee0c30b9c5a0ba4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-06-06T21:04:08Z",
    "title_canon_sha256": "335ec834ee579d75d8226fab8829f6f3d97e2759e251a92224d77d1ada70d60f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.01979",
    "kind": "arxiv",
    "version": 1
  }
}