Pith Number

pith:EEKKADQ5

pith:2026:EEKKADQ5GPPKV6IVJZQ44BRCUL

not attested not anchored not stored refs pending

Non-uniqueness of geodesic limits and a question of Grayson and Gage

Shrey Aryan, Tang-Kai Lee

arxiv:2608.04855 v1 · 2026-08-05 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EEKKADQ5GPPKV6IVJZQ44BRCUL}

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	2026-08-06T01:47:24.421905Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2114a00e1d33deaaf9154e61ce0622a2d8780b78ea91cb7cf7487a237392c5f1

Aliases

arxiv: 2608.04855 · arxiv_version: 2608.04855v1 · doi: 10.48550/arxiv.2608.04855 · pith_short_12: EEKKADQ5GPPK · pith_short_16: EEKKADQ5GPPKV6IV · pith_short_8: EEKKADQ5

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/EEKKADQ5GPPKV6IVJZQ44BRCUL \
  | 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: 2114a00e1d33deaaf9154e61ce0622a2d8780b78ea91cb7cf7487a237392c5f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7894a8a923b2415fc6745ec0cefb86e37387c357d649dbd942ccd5a82cae6546",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-08-05T13:48:07Z",
    "title_canon_sha256": "a1ee2eb7f622ec786698997b1a857070a2cd94dd2e8ca6e121c986855f1908dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04855",
    "kind": "arxiv",
    "version": 1
  }
}