Pith Number

pith:AFXX4EGS

pith:2016:AFXX4EGSYB5PNEOPICUKFX4MOB

not attested not anchored not stored refs pending

Two-Spectra Theorem with Uncertainty

Alexei Poltoratski, Nikolai Makarov

arxiv:1612.05165 v6 · 2016-12-15 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFXX4EGSYB5PNEOPICUKFX4MOB}

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	2026-05-18T00:27:09.783047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

016f7e10d2c07af691cf40a8a2df8c705d9876fcb942f3e17e9258b486203752

Aliases

arxiv: 1612.05165 · arxiv_version: 1612.05165v6 · doi: 10.48550/arxiv.1612.05165 · pith_short_12: AFXX4EGSYB5P · pith_short_16: AFXX4EGSYB5PNEOP · pith_short_8: AFXX4EGS

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/AFXX4EGSYB5PNEOPICUKFX4MOB \
  | 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: 016f7e10d2c07af691cf40a8a2df8c705d9876fcb942f3e17e9258b486203752

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22355d307b54ee962b23a8b074fb9afd19ce16450f1fccfa942d3050f915193c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-12-15T17:47:34Z",
    "title_canon_sha256": "2b47f9c1c06a2075cc583166654430cc6422752d5a9b3a02d06eeeff8434d006"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05165",
    "kind": "arxiv",
    "version": 6
  }
}