Pith Number

pith:VXHJZSXM

pith:2026:VXHJZSXM65QCCN2RKHL42K2V2F

not attested not anchored not stored refs pending

Trace spectra of simplices in large sets

Alexander Fish, Michael Bj\"orklund, Shrey Sanadhya

arxiv:2606.12947 v1 · 2026-06-11 · math.DS · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXHJZSXM65QCCN2RKHL42K2V2F}

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	2026-06-12T01:09:35.223987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adce9ccaecf76021375151d7cd2b55d1799369dd0d54f77c78047ce7aca1e1ca

Aliases

arxiv: 2606.12947 · arxiv_version: 2606.12947v1 · doi: 10.48550/arxiv.2606.12947 · pith_short_12: VXHJZSXM65QC · pith_short_16: VXHJZSXM65QCCN2R · pith_short_8: VXHJZSXM

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/VXHJZSXM65QCCN2RKHL42K2V2F \
  | 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: adce9ccaecf76021375151d7cd2b55d1799369dd0d54f77c78047ce7aca1e1ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da12522d774ffe8c31f2a8a73578d896cbe4cf1d5ec04324f205a5d4cd755d7c",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-11T06:20:02Z",
    "title_canon_sha256": "fe2ca4f7d7ab491b44833f2ed99f1e02926bf5dae7bfa99b09d5b56dcf915b8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12947",
    "kind": "arxiv",
    "version": 1
  }
}