Pith Number

pith:WK7XYUHW

pith:2004:WK7XYUHWTDPNL6ML7UMPCTPCQG

not attested not anchored not stored refs pending

Bounds on the spectral shift function and the density of states

Dirk Hundertmark, Ivan Veselic', Peter Stollmann, Rowan Killip, Shu Nakamura

arxiv:math-ph/0412078 v1 · 2004-12-21 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WK7XYUHWTDPNL6ML7UMPCTPCQG}

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	2026-05-18T01:23:17.170819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2bf7c50f698ded5f98bfd18f14de281851fe1e305dcb76ac3ac4ed75103639e

Aliases

arxiv: math-ph/0412078 · arxiv_version: math-ph/0412078v1 · doi: 10.48550/arxiv.math-ph/0412078 · pith_short_12: WK7XYUHWTDPN · pith_short_16: WK7XYUHWTDPNL6ML · pith_short_8: WK7XYUHW

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/WK7XYUHWTDPNL6ML7UMPCTPCQG \
  | 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: b2bf7c50f698ded5f98bfd18f14de281851fe1e305dcb76ac3ac4ed75103639e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d582be51d27a073ad61c28f31ce4c1b6a01a2dc75033948df47121a7e22106a9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2004-12-21T22:41:15Z",
    "title_canon_sha256": "304054dd769b8f73b5d07f00e2e1403bce2dc63bc63532de45efa32d72dadb43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0412078",
    "kind": "arxiv",
    "version": 1
  }
}