Versioned Protected-Data Exports and Cross-Volume Round Trips

Protected data can move safely between subjects only when the exported object carries its theory definition, protection mechanism, conventions, scope, provenance, uncertainty, semantic version, and content hash. A bare list of dimensions or central charges invites normalization drift and stronger downstream claims than the source supports. This page defines a compact, content-addressed record and a round trip that preserves those boundaries, following the general findability and provenance discipline of the FAIR principles Wilkinson et al. 2016.

Required background. Use the normalization discipline of the AGT dictionary and the information-loss analysis of the four-dimensional chiral-algebra sector.

Helpful background. Protected SCFT data for bootstrap use shows how a neighboring subject consumes only a selected subset.

The export is a typed scientific object

A protected-data record should answer five questions without consulting prose:

1. What theory? Dimension, supersymmetry, global form, deformation point, and any defect or background.
2. What quantity? Operator, algebra, anomaly, index coefficient, partition function, or category-level datum.
3. Why exact? Shortening, Q-cohomology, anomaly, localization, holomorphy, or a stated combination.
4. In which convention? Generator normalization, charge basis, scale, counterterms, fugacities, and parameter map.
5. How far does it reach? Included claims, excluded inferences, uncertainty, unresolved fields, and source cutoff.

The minimal field groups are:

Field group	Required content
theory	Human-readable identity and complete global/background qualifiers
observable	Kind, sector, arguments, units, and normalization
values	Exact expressions or numerical values with uncertainty
protection	Mechanism for each exported value
conventions	Charge, anomaly, operator, and scheme conventions
scope	Explicit inclusions and exclusions
sources	Stable routes or primary references with locators
source_cutoff	Latest evidence date represented by the record
unresolved	Named unknowns with reasons, never silent nulls
versions and hash	Schema compatibility and content identity

A canonical Argyres–Douglas example

The following record exports a bounded subset of the $(A_1,A_2)$ theory card. Rational numbers are strings so no binary floating-point conversion occurs.

{
  "schema_version": "1.0.0",
  "record_version": "1.0.0",
  "theory": {
    "dimension": 4,
    "name": "(A1,A2) Argyres-Douglas SCFT",
    "supersymmetry": "N=2"
  },
  "observable": {
    "kind": "protected_theory_card",
    "sectors": ["Coulomb", "Schur"]
  },
  "values": {
    "a": "43/120",
    "c": "11/30",
    "c_2d": "-22/5",
    "delta_u": "6/5"
  },
  "protection": ["N=2 shortening", "Weyl anomaly", "Q-cohomology"],
  "conventions": {
    "chiral_algebra": "c_2d = -12 c_4d",
    "weyl_anomalies": "a,c normalized so a free N=2 vector has (5/24,1/6)"
  },
  "scope": {
    "includes": [
      "rank-one Coulomb data",
      "conformal anomalies",
      "chiral-algebra central charge"
    ],
    "excludes": ["long-multiplet spectrum", "generic OPE coefficients"]
  },
  "sources": [
    "/supersymmetry-duality/n2-seiberg-witten/argyres-douglas-class-s-interfaces/",
    "/supersymmetry-duality/protected-operators-defects-correspondences/chiral-algebra-correspondence/"
  ],
  "source_cutoff": "2026-08-10",
  "uncertainty": {"kind": "exact"},
  "unresolved": [],
  "content_hash": {
    "algorithm": "sha256",
    "canonicalization": "RFC 8785",
    "excluded_field": "content_hash",
    "value": "9a46b62d218a75be4824188c2c2ba6e01f4fd6dae50841f7e0652866dc2e024e"
  }
}

The hash is computed from the RFC 8785 canonical JSON representation after removing the content_hash field. It binds values, conventions, scope, sources, and cutoff together. Reordering object keys or changing whitespace leaves the canonical hash fixed; changing an array order or scientific value changes it RFC 8785, §§3–4.

The record contains enough redundancy for scientific checks:

$$-12c=-12\left(\frac{11}{30}\right)=-\frac{22}{5}=c_{2d},$$

and the Coulomb dimension obeys the rank-one relation

$$2a-c=\frac{2\Delta_u-1}{4}=\frac7{20}.$$

Schema validity alone would not catch a wrong sign in either identity, so semantic checks accompany structural validation.

Semantic versions and compatibility

Use semantic versions according to the meaning of the record:

• increment the patch version for source-locator or explanatory corrections that do not change values or interpretation;
• increment the minor version for backward-compatible added fields or new protected values;
• increment the major version when a normalization, field meaning, theory specification, or required schema changes incompatibly.

Every scientific change produces a new content hash even when it is backward compatible. Version numbers describe compatibility; hashes identify exact content. Neither substitutes for the other.

If an exact value is corrected, retain the superseded record and mark the replacement relationship. Silent mutation breaks reproducibility for every downstream calculation that cited the old hash.

The cross-volume round trip

A consumer should import the tuple

$$(\text{schema version},\text{record version},\text{content hash})$$

and return a derived record containing:

• the source tuple unchanged;
• the transformation name, version, parameters, and code or analytic formula;
• the subset of source fields actually used;
• derived values with propagated uncertainty;
• any information discarded by the transformation;
• the strongest allowed downstream claim.

For example, a conformal-bootstrap calculation may use $c$, flavor levels, and selected protected OPE data. It must not claim that the source supplied long-operator dimensions if the source scope excludes them. When a newer source hash appears, the consumer can determine mechanically whether its result is stale and whether the changed fields were among those used.

Provenance should describe entities, activities, and derivations rather than only naming a file. This structure follows the same separation formalized by the W3C provenance model W3C PROV-DM 2013, §§2–3.

Validation before publication

Run four layers of checks:

1. Structural: required keys, types, enumerations, and version syntax.
2. Referential: every source route and external locator resolves to the intended object.
3. Semantic: dimensions, charge bases, anomaly identities, exact relations, and limiting cases agree.
4. Cryptographic: canonicalize independently and reproduce the declared digest.

Then simulate one consumer round trip. Change a source field deliberately and confirm that the hash changes and the consumer marks its derivative stale. Change only JSON whitespace and confirm that the canonical hash does not change.

What each protected export preserves and loses

A protected result is portable only together with the hypotheses, normalization, information loss, ambiguity, uncertainty, and evidence status that make it meaningful. The table compares five export profiles: three reusable contracts and two executable, content-bound records. Read across one row before reusing any entry; exact arithmetic does not strengthen the scientific status stated in that row.

Protected quantities, information loss, ambiguity, evidence status, and version boundaries

Protected object	Protected quantity	Mechanism, hypotheses, and normalization	Discarded information	Remaining ambiguity	Uncertainty	Theorem, evidence, or conjecture status	Source cutoff	Consumer contract	Export version
Q-cohomology export contract with operator mixing resolved	Protected quantityThe class in ker Q / im Q and separated cohomological correlator data after exact and zero-norm directions are removed.	Mechanism, hypotheses, and normalizationQ squared vanishes on the selected gauge-invariant sector; the state and measure are Q-invariant; no contact or boundary term survives; the induced two-point form and charge sector are declared.	Discarded informationThe representative, Q-exact descendants, null directions, generic noncohomological correlators, and unprotected spacetime dependence.	Remaining ambiguityThe induced form fixes norms, but a degenerate invariant subspace still permits unitary basis rotations; comparison along parameter space additionally requires a connection or Berry holonomy.	UncertaintyNo numerical error is implied. A surviving contact term, boundary contribution, accidental symmetry, or singular mixing form invalidates the claimed descent instead of enlarging it.	Theorem, evidence, or conjecture statusConditional theorem: the quotient and Ward-identity descent are exact under the stated cohomological and separated-insertion hypotheses.	Source cutoff2026-09-04	Consumer contractExport Q, conserved charges, relation matrix, induced Gram form, basis or invariant subspace, and every unresolved null or contact direction; never export a bare operator label as the protected object.	Export versionShared comparison record 1.0.0; no standalone cohomology payload is issued in this edition.
Chiral-ring presentation export contract	Protected quantityNormalized generators and the complete exact relation ideal, including quantum deformations, nilpotents, and branch data when present.	Mechanism, hypotheses, and normalizationQ-cohomology and holomorphy with the theory, vacuum branch, generator normalization, holomorphic scale, and equation-of-motion quotient fixed.	Discarded informationKähler geometry, generic nonchiral correlators, and—if only the reduced variety is exported—nilpotent operator products and embedded branch structure.	Remaining ambiguityNone within the named presentation. Comparison with another presentation requires explicit polynomial maps and inverses; without them, generator rescalings, scale conventions, branch matching, and primary decomposition remain underdetermined.	UncertaintyA displayed holomorphic relation can be exact while completeness of the presentation or a proposed ring isomorphism remains an additional proof obligation.	Theorem, evidence, or conjecture statusEstablished protected relation in the cited SQCD fixture; equivalence of two full ring presentations requires a separately checked inverse and does not follow from matching reduced varieties.	Source cutoff2026-09-04	Consumer contractExport generators, the full nonreduced ideal, charge and scale conventions, branch decomposition, and forward and inverse generator maps; state explicitly if only a reduced vacuum variety is consumed.	Export versionShared comparison record 1.0.0; no standalone chiral-ring payload is issued in this edition.
BPS-line observable export contract	Protected quantityA declared expectation value, framed index, fusion coefficient, difference-operator action, or defect correlator on its stated background—not all defect data at once.	Mechanism, hypotheses, and normalizationGlobal gauge form, trajectory, scalar coupling or disorder singularity, preserved supercharge, electric-magnetic label, screening quotient, framing, counterterms, bubbling sectors, and normalization are fixed.	Discarded informationGeneric unprotected defect-CFT data, regulator-dependent perimeter terms, and any observable not named by the export.	Remaining ambiguityNone within a fully specified export. When importing a result from another convention, its global form, genuine-line lattice, screening quotient, discrete theta angle, framing, counterterms, contour, and bubbling normalization must be translated explicitly; missing metadata makes the comparison underdetermined.	UncertaintyExactness belongs only to the selected protected quantity. Contour evaluation, bubbling data, and subtraction prescriptions can retain computational or scheme uncertainty.	Theorem, evidence, or conjecture statusThe operator definition is exact once its global and singularity data are fixed; each evaluated value inherits the theorem, localization-evidence, or conjecture status of its named calculation.	Source cutoff2026-09-04	Consumer contractExport the complete line specification, background, renormalization and framing convention, bubbling sum, selected observable, and duality map; do not replace these fields by an isolated charge pair.	Export versionShared comparison record 1.0.0; no standalone line-observable payload is issued in this edition.
Normalized A1 AGT one-instanton/block fixture	Protected quantityAt the frozen nonpolar rational point, the q^1 identity z1 + nu = F1 with z1 = -1217173/658350, nu = 7/3, and F1 = 318977/658350.	Mechanism, hypotheses, and normalizationThe U(2) two-antifundamental/two-fundamental orientation, Coulomb pair (a,-a), Omega scale, insertion order, ultraviolet q coordinate, Virasoro Gram normalization, and Abelian factor (1-q)^nu are frozen.	Discarded informationHigher instanton levels, series convergence and global analytic continuation, the complete S4 gluing problem, higher rank, other punctures, and unprotected observables of either parent theory.	Remaining ambiguityNone in the frozen formal q^1 fixture. Translating another convention can change mass shifts, the U(2)/SU(2) split, Abelian factor, external-weight order, and q coordinate; analytic continuation beyond this fixture also requires a logarithm branch and a localization contour.	UncertaintyZero arithmetic uncertainty at one exact rational point; the test has a strict q^1 scope and supplies no error estimate or evidence for omitted orders.	Theorem, evidence, or conjecture statusExact independent rational calculation at q^1. The original all-level AGT statement is a conjecture with extensive checks and setting-specific algebraic constructions; no full-theory equivalence follows.	Source cutoff2026-09-04	Consumer contractImport the benchmark id and byte hash together with the matter orientation, mass map, Omega scale, insertion order, q convention, U(1) exponent, exact values, and explicit claim ceiling.	Export versionAGT benchmark schema 1.0.0; benchmark qft.benchmark.supersymmetry-duality.agt-u2-nf4-one-instanton.v1.
Content-addressed protected-SCFT bundle and Volume 9 round trip	Protected quantityThe N=1 SU(3), Nf=6 record's stored anomaly traces, a, c, C_T, flavor-current coefficients, and three selected chiral-multiplet identities under its conditional fixed-point claim.	Mechanism, hypotheses, and normalizationDraft 2020-12 schema validation, RFC 8785 content and convention hashes, exact forward/inverse normalization maps, the declared global form and R-current, and the source-record scope are all checked.	Discarded informationUnit-normalized non-Ward OPE coefficients, index multiplicities, partition functions, long-multiplet gaps, a complete external-correlator problem, and a proof of fixed-point existence or uniqueness.	Remaining ambiguityNo ambiguity remains in the stored fields or checked normalization maps. Baryon-basis choices and Gram matrices are absent, index inversion is nonunique, and any consumer transformation without an inverse map creates new convention ambiguity.	UncertaintyThe stored algebraic values are exact conditional on the standard interacting fixed-point identification; no numerical covariance is present, and the dynamical existence and uniqueness caveat remains.	Theorem, evidence, or conjecture statusSchema, hash, arithmetic, and round-trip verification are exact mechanical checks; the scientific values retain the source record's conditional duality-supported evidence status.	Source cutoff2026-08-24	Consumer contractImport the schema-version, record-version, and content-hash tuple unchanged; verify every forward and inverse map; return used and discarded fields, propagated uncertainty, and the strongest allowed downstream claim.	Export versionProtected-SCFT schema 1.0.0; record 1.0.0; content SHA-256 68a67e66c43e4d0a258f0d26b0b9c08c6164922be256a41112bb5761ee582910.

The evidence trail is the cited exposition on cohomology and mixing, chiral rings, BPS line observables, the AGT benchmark, and the protected-data round trip. The last two rows additionally bind the exact AGT JSON fixture, the content-addressed N=1 SU(3), Nf=6 record, and its Volume 9 consumer.

Download the canonical JSON record, download the reader-visible CSV projection, or inspect the JSON Schema. The CSV contains only the row ID and ten displayed columns; source relationships, independent checks, evidence bindings, and hashes live in the JSON record and provenance.

Inference boundary. A downstream claim stops at the exact object, hypotheses, normalization, evidence status, uncertainty, and version in its row. In particular, an index coefficient cannot become an unsigned multiplicity or OPE coefficient, an integrated localization observable cannot become a separated correlator, and a checked correspondence coefficient cannot become a full-theory equivalence without a separately validated map.

Failure modes

Hidden normalization. A central charge without the free-field convention can differ by a fixed factor across subjects.

False exactness. A numerical fit or conjectural correspondence must carry uncertainty and status rather than being serialized as an exact rational.

Unresolved mixing erased. Export a protected combination or equivalence class when individual operators are not separated.

Scope strengthened downstream. A protected algebra does not export a full spectrum, and an index does not export unsigned multiplicities.

Hash refreshed without review. A new digest confirms new bytes, not scientific correctness. Semantic checks must pass first.

Stale sources hidden. The source cutoff and exact source locators make later corrections discoverable.

Exercises

Verify the two internal identities in the example record.

Solution

First, $-12(11/30)=-132/30=-22/5$. Second, $2(43/120)-11/30=86/120-44/120=42/120=7/20$, while $(2(6/5)-1)/4=(12/5-1)/4=7/20$.

References

• Moreau, L., and P. Missier, eds. PROV-DM: The PROV Data Model. W3C Recommendation, 30 April 2013. W3C.
• Rundgren, A., B. Jordan, and S. Erdtman. JSON Canonicalization Scheme (JCS). RFC 8785, June 2020. RFC Editor.
• Wilkinson, M. D., et al. “The FAIR Guiding Principles for Scientific Data Management and Stewardship.” Scientific Data 3 (2016): 160018. DOI.