Pith Number

pith:GT54ZJPD

pith:2016:GT54ZJPDUKPQW3RONNRODMEFWQ

not attested not anchored not stored refs pending

Strong submultiplicativity of the Poincare metric

Daniela Kraus, Oliver Roth

arxiv:1603.06818 v1 · 2016-03-22 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GT54ZJPDUKPQW3RONNRODMEFWQ}

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	2026-05-18T01:18:34.634332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9

Aliases

arxiv: 1603.06818 · arxiv_version: 1603.06818v1 · doi: 10.48550/arxiv.1603.06818 · pith_short_12: GT54ZJPDUKPQ · pith_short_16: GT54ZJPDUKPQW3RO · pith_short_8: GT54ZJPD

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/GT54ZJPDUKPQW3RONNRODMEFWQ \
  | 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: 34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56de62c54dab8a77faddab6fb6c8dcabe40d2c050c0b4cc909d9c46bc2c6317f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2016-03-22T15:07:01Z",
    "title_canon_sha256": "3d457f1ebc23187f77b20653fbd5d8e1865323a6958c2e705bd4e59fba0f89ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06818",
    "kind": "arxiv",
    "version": 1
  }
}