Pith Number

pith:5GDXEQSF

pith:2011:5GDXEQSFO4ZQNPBTDI6JKXAP3F

not attested not anchored not stored refs pending

Momentum Operators in Two Intervals: Spectra and Phase Transition

Feng Tian, Palle E. T. Jorgensen, Steen Pedersen

arxiv:1110.5948 v1 · 2011-10-26 · math.SP · math-ph · math.AP · math.CA · math.FA · 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{5GDXEQSFO4ZQNPBTDI6JKXAP3F}

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	2026-05-18T03:55:46.875423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e987724245773306bc331a3c955c0fd97d445791d0310bcab3920a40905d391e

Aliases

arxiv: 1110.5948 · arxiv_version: 1110.5948v1 · doi: 10.48550/arxiv.1110.5948 · pith_short_12: 5GDXEQSFO4ZQ · pith_short_16: 5GDXEQSFO4ZQNPBT · pith_short_8: 5GDXEQSF

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/5GDXEQSFO4ZQNPBTDI6JKXAP3F \
  | 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: e987724245773306bc331a3c955c0fd97d445791d0310bcab3920a40905d391e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f817692d8881ce06bfddc80326a022a40651652c5a6651c9889891eb6459ee",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.CA",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-10-26T23:46:49Z",
    "title_canon_sha256": "2dd8e31161d85ac9fd42368fe5939e6a54c0a41e94f3b924e040f6b25ce49760"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5948",
    "kind": "arxiv",
    "version": 1
  }
}