Pith Number

pith:F73ZAJYO

pith:2025:F73ZAJYOF6JZDSL3VXYHWSOCTU

not attested not anchored not stored refs pending

Proof of Existence of Integers Excluding Two Residue Values in a Specific Range

Liang Zhao

arxiv:2501.15707 v1 · 2025-01-27 · 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{F73ZAJYOF6JZDSL3VXYHWSOCTU}

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	2026-07-05T10:05:33.171337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ff790270e2f9391c97badf07b49c29d1271977efb3112ca0de2ada47138aa5a

Aliases

arxiv: 2501.15707 · arxiv_version: 2501.15707v1 · doi: 10.48550/arxiv.2501.15707 · pith_short_12: F73ZAJYOF6JZ · pith_short_16: F73ZAJYOF6JZDSL3 · pith_short_8: F73ZAJYO

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/F73ZAJYOF6JZDSL3VXYHWSOCTU \
  | 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: 2ff790270e2f9391c97badf07b49c29d1271977efb3112ca0de2ada47138aa5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f4180fc0c3ea617eab54da5c7cbf915153cbb18256f1907084186a0260b980c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-01-27T00:01:03Z",
    "title_canon_sha256": "b5b7bd075222a8dcd5d6d38a89128c5e2cd760b53a79574c438da405fc0ae824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.15707",
    "kind": "arxiv",
    "version": 1
  }
}