Pith Number

pith:NP32O757

pith:2015:NP32O757SODKKKV5DSUM42JWIL

not attested not anchored not stored refs pending

Fixed-energy harmonic functions

Aaron Abrams, Richard Kenyon

arxiv:1505.05785 v3 · 2015-05-21 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NP32O757SODKKKV5DSUM42JWIL}

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	2026-05-18T00:28:57.244331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bf7a77fbf9386a52abd1ca8ce693642da62f6ab3cd6736bc294d43f1b726ed3

Aliases

arxiv: 1505.05785 · arxiv_version: 1505.05785v3 · doi: 10.48550/arxiv.1505.05785 · pith_short_12: NP32O757SODK · pith_short_16: NP32O757SODKKKV5 · pith_short_8: NP32O757

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/NP32O757SODKKKV5DSUM42JWIL \
  | 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: 6bf7a77fbf9386a52abd1ca8ce693642da62f6ab3cd6736bc294d43f1b726ed3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f873b76370b09ab3890ead28f6e23c470c863c294ca2b6f3613764db35200e0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-05-21T16:50:47Z",
    "title_canon_sha256": "2f48b8bb2fae174ac23e010e683889fce7a51106b0de8621fcf6a70998a86fe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05785",
    "kind": "arxiv",
    "version": 3
  }
}