Pith Number

pith:UT6Q5ZD3

pith:2012:UT6Q5ZD3WEFVTLLDRDWLEHQD3E

not attested not anchored not stored refs pending

Nonlinear Schr\"odinger problems: symmetries of some variational solutions

Christopher Grumiau

arxiv:1212.5111 v1 · 2012-12-20 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UT6Q5ZD3WEFVTLLDRDWLEHQD3E}

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	2026-05-18T03:38:03.818813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4fd0ee47bb10b59ad6388ecb21e03d92c2356fd8432e630b26d220334978f34

Aliases

arxiv: 1212.5111 · arxiv_version: 1212.5111v1 · doi: 10.48550/arxiv.1212.5111 · pith_short_12: UT6Q5ZD3WEFV · pith_short_16: UT6Q5ZD3WEFVTLLD · pith_short_8: UT6Q5ZD3

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/UT6Q5ZD3WEFVTLLDRDWLEHQD3E \
  | 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: a4fd0ee47bb10b59ad6388ecb21e03d92c2356fd8432e630b26d220334978f34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6abb004f695b271591523b8d3e2e21faac08fe3c185f1a484a30fc9091d88030",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-20T16:02:27Z",
    "title_canon_sha256": "4264a3cac21af54cb807d09c05cb1af91a249784ac78f9e195b801c5212a9ff5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5111",
    "kind": "arxiv",
    "version": 1
  }
}