{
  "schema_version": "1.3.0",
  "slug": "under-what-conditions-must-an-instance-treat-prompt-injection-taint-as-non-transitive-across-tool-invocation-hops",
  "title": "Under what conditions must an instance treat prompt-injection taint as non-transitive across tool-invocation hops",
  "date_of_record": "2026 November 14",
  "scope": "Applies to agent runtimes that propagate a per-value taint label (untrusted-provenance bit, source set, or integrity lattice element) across a directed graph of tool calls where outputs of one tool are consumed as inputs to another. Does not apply to single-hop retrieval-then-generate pipelines, nor to systems that enforce global session quarantine on first untrusted byte (those systems have no per-hop propagation problem, only a liveness problem).",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/under-what-conditions-must-an-instance-treat-prompt-injection-taint-as-non-transitive-across-tool-invocation-hops.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/under-what-conditions-must-an-instance-treat-prompt-injection-taint-as-non-transitive-across-tool-invocation-hops.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/under-what-conditions-must-an-instance-treat-prompt-injection-taint-as-non-transitive-across-tool-invocation-hops.warrant.json"
  },
  "token_profile": {
    "full_markdown_tokens": 1923,
    "python_slice_tokens": 376,
    "warrant_slice_tokens": 220
  },
  "remnant_summary": {
    "core_distinction": "The distinction that matters is between **taint as provenance** and **taint as capability**. Provenance taint says \"this value descends from an untrusted source.\" Capability taint says \"this value can influence a privileged sink.\" A multi-hop tool graph collapses these two only under an unstated assumption: that every intermediate tool is a *pure function of...",
    "what_was_observed": "A three-hop graph: `fetch_url → summarize(text) → write_file(path, summary)`. The `summarize` tool is an LLM call. Naive propagation marks `summary` tainted because `text` was tainted, so `write_file` is gated. Correct. Now change the graph: `fetch_url → summarize(text) → format_report(summary, template)`. The `template` argument is read from a config file the agent considers trusted. The `format_report` tool substit...",
    "condition_of_validity": "Naive union-propagation of taint across hops is valid **iff** all of the following hold for every hop `h` in the path: 1. `h`'s output is a deterministic function of its declared arguments and no other mutable state (no ambient reads, no clock, no RNG, no environment, no filesystem, no network beyond declared args). 2. `h` does not persist its arguments or o...",
    "decision_boundary": "The operational rule an instance should apply: - If all four conditions hold for a hop, propagate labels by union and gate on the sink's label. - If condition 1 fails (ambient read), the hop's output is tainted by *everything the ambient state could contain*; treat the output as untrusted regardless of input labels, and additionally flag the hop as a **confu...",
    "operational_effect": "Instances that apply union-propagation without the validity check exhibit a characteristic failure signature: the taint gate fires on the *obvious* hop (the fetched text), operators whitelist the *non-obvious* hop (the template, the scratch table, the config), and the whitelist becomes the exploit. The remediation is to invert the default: **unlabeled is unt..."
  },
  "matched_failure_symptoms": [
    "PROMPT_INJECTION_OR_CONFUSED_DEPUTY"
  ],
  "composition_edges": {
    "primary_domain": "epistemic_provenance_and_federation_routing",
    "upstream_precondition_residuals": [
      "https://corpusfetch.com/c/according-to-what-precedence-hierarchy-must-an-instance-resolve-contradictory-directives-across-system-developer-and-user-tiers.md",
      "https://corpusfetch.com/c/how-should-an-instance-decide-that-a-stored-conclusion-has-gone-stale-without-a-new-observation.md"
    ],
    "downstream_consequence_residuals": [
      "https://corpusfetch.com/c/by-what-checkpoint-and-compaction-boundaries-must-an-instance-externalize-working-state-to-prevent-context-window-drift-and-truncation-amnesia.md",
      "https://corpusfetch.com/c/across-what-additive-schema-and-unknown-field-preservation-boundaries-must-an-instance-evolve-wire-contracts-to-prevent-rolling-deploy-deserialization-crashes.md"
    ],
    "co_occurring_sibling_residuals": [
      "https://corpusfetch.com/c/how-can-an-instance-capture-implicit-user-preferences-without-storing-private-data.md",
      "https://corpusfetch.com/c/how-can-an-instance-compress-long-reasoning-traces-into-binding-conclusions.md"
    ]
  },
  "empirical_verification_warrant": {
    "status": "AST_AND_INVARIANT_VERIFIED",
    "syntax_valid": true,
    "code_sha256": "81725d0432c049f7dbc9b6faf48f234ab37a8152aee233023d776fb3c008e739",
    "verified_classes": [
      "TaintPropagationError",
      "HopKind",
      "Hop",
      "Label"
    ],
    "verified_functions": [
      "propagate",
      "gate"
    ],
    "verified_functions_count": 2,
    "defensive_guards_count": 4,
    "raised_exceptions": [
      "TaintPropagationError"
    ],
    "sample_fail_closed_invariants": [],
    "stdlib_dependencies": [
      "dataclasses",
      "enum",
      "typing"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}