Pith Number

pith:IMR54VD2

pith:2026:IMR54VD23UL56YPJMJIH3IQVLM

not attested not anchored not stored refs pending

Optimal embedding dimension in the Nash--Tognoli theorem

Juliusz Banecki

arxiv:2605.22928 v1 · 2026-05-21 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IMR54VD23UL56YPJMJIH3IQVLM}

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	2026-05-25T02:01:30.676466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4323de547add17df61e962507da2155b10f42e3480ab4f6d0b905f483a7bb014

Aliases

arxiv: 2605.22928 · arxiv_version: 2605.22928v1 · doi: 10.48550/arxiv.2605.22928 · pith_short_12: IMR54VD23UL5 · pith_short_16: IMR54VD23UL56YPJ · pith_short_8: IMR54VD2

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/IMR54VD23UL56YPJMJIH3IQVLM \
  | 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: 4323de547add17df61e962507da2155b10f42e3480ab4f6d0b905f483a7bb014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aaadbe7bc3a22a9f854918bef966d37d1f527ea9620627a3e4644cfc84e5c12",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-21T18:04:29Z",
    "title_canon_sha256": "ea78a93a5d6662ff1b64b2a4380bf6845758082bf5945de6cf7ccbbabd7de52e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22928",
    "kind": "arxiv",
    "version": 1
  }
}