Pith Number

pith:4TH3HAIP

pith:2026:4TH3HAIPGLFJFNRTTHZU32GCJF

not attested not anchored not stored refs pending

On the embedding rigidity problem for uniformly locally finite coarse spaces

Teng Zhang

arxiv:2607.16949 v1 · 2026-07-18 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TH3HAIPGLFJFNRTTHZU32GCJF}

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	2026-07-21T01:21:07.773060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4cfb3810f32ca92b63399f34de8c2496c60ae25d370ee5bd55b48e5061c83a9

Aliases

arxiv: 2607.16949 · arxiv_version: 2607.16949v1 · doi: 10.48550/arxiv.2607.16949 · pith_short_12: 4TH3HAIPGLFJ · pith_short_16: 4TH3HAIPGLFJFNRT · pith_short_8: 4TH3HAIP

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/4TH3HAIPGLFJFNRTTHZU32GCJF \
  | 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: e4cfb3810f32ca92b63399f34de8c2496c60ae25d370ee5bd55b48e5061c83a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f53ed1b62e207deb1ec5ebf4966621c9f6ac94dffbdb5a51826a4df9e419071",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-18T20:04:54Z",
    "title_canon_sha256": "3eb4c067cd2a8722f7a0454a6176844535a48f3ddab49df95cef0e5fe3cfffb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16949",
    "kind": "arxiv",
    "version": 1
  }
}