Pith Number

pith:KOWDRHUB

pith:2026:KOWDRHUB7PYA3233ZUELRO2Q4B

not attested not anchored not stored refs pending

Grothendieck's theorem for Bessel sequences

Lukas Liehr, Mitchell A. Taylor, Peiyang Yu

arxiv:2608.12280 v1 · 2026-08-12 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KOWDRHUB7PYA3233ZUELRO2Q4B}

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	2026-08-13T01:30:42.317524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53ac389e81fbf00deb7bcd08b8bb50e042526f4c1287830decd745f14a0205bd

Aliases

arxiv: 2608.12280 · arxiv_version: 2608.12280v1 · doi: 10.48550/arxiv.2608.12280 · pith_short_12: KOWDRHUB7PYA · pith_short_16: KOWDRHUB7PYA3233 · pith_short_8: KOWDRHUB

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/KOWDRHUB7PYA3233ZUELRO2Q4B \
  | 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: 53ac389e81fbf00deb7bcd08b8bb50e042526f4c1287830decd745f14a0205bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21d5febd3dd3fbbc535444813e4bba21dd4ffec6af1e860ea5d1761c2b8849c5",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-12T17:23:03Z",
    "title_canon_sha256": "76cf072ea563a68169b8a589403e16479a420a84a89402ad4c0c41bac56bc5bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12280",
    "kind": "arxiv",
    "version": 1
  }
}