{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:W4ITPBL266ORXAVR4HLM5ODG2T","short_pith_number":"pith:W4ITPBL2","canonical_record":{"source":{"id":"quant-ph/0703060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-03-07T16:00:51Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"e86ca58747a80ac7bb25f6b9f2ef9d76c8a5f0211056bd06d41b6dd4f6eada72","abstract_canon_sha256":"7b71372d576f02718bccbaa5a4335d2ff179348ae89a0199705fad76b970f5d7"},"schema_version":"1.0"},"canonical_sha256":"b71137857af79d1b82b1e1d6ceb866d4f45bb8ff80081988ea93eb3d96d8f9c1","source":{"kind":"arxiv","id":"quant-ph/0703060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0703060","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0703060v1","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0703060","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"W4ITPBL266OR","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"W4ITPBL266ORXAVR","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"W4ITPBL2","created_at":"2026-07-04T15:31:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:W4ITPBL266ORXAVR4HLM5ODG2T","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0703060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-03-07T16:00:51Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"e86ca58747a80ac7bb25f6b9f2ef9d76c8a5f0211056bd06d41b6dd4f6eada72","abstract_canon_sha256":"7b71372d576f02718bccbaa5a4335d2ff179348ae89a0199705fad76b970f5d7"},"schema_version":"1.0"},"canonical_sha256":"b71137857af79d1b82b1e1d6ceb866d4f45bb8ff80081988ea93eb3d96d8f9c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:31:51.821947Z","signature_b64":"EheGHuIUmUiw2/m0Pwy/FxG4kHQF2CMoHtnIgyk/3rpAUuo/O8c/GsbNFzfV5IaRHn+pQYWP9pQ6eb8DX0SWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b71137857af79d1b82b1e1d6ceb866d4f45bb8ff80081988ea93eb3d96d8f9c1","last_reissued_at":"2026-07-04T15:31:51.821528Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:31:51.821528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0703060","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+A6BI/06Q3dg9ZmU5sbxujioVo9sSJXSLkwr5LxQsCZgOlQJV7GL5oFVCG9fEMFO50vUwR5vn49mQMNY92yAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:40:44.901194Z"},"content_sha256":"488c36da8cba7c390c37a22b622399a8713622b1b4281320321af000174b28cb","schema_version":"1.0","event_id":"sha256:488c36da8cba7c390c37a22b622399a8713622b1b4281320321af000174b28cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:W4ITPBL266ORXAVR4HLM5ODG2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Topos Foundation for Theories of Physics: I. Formal Languages for Physics","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A. Doering, C.J. Isham","submitted_at":"2007-03-07T16:00:51Z","abstract_excerpt":"This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper we discuss two different types of language "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0703060","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0703060/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmcIMcQnOK5E8qA/Vevh58sbbxkY6Gzoz71s8aKV0cqwMzm6RIIvhat6MP52pwCWz/pLGhGmpLfllTIQfMFACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:40:44.901727Z"},"content_sha256":"0fe571d8e7bbfe79a5a0ebe01b6c0045fff2520ee1db1a86bcd210ba87225211","schema_version":"1.0","event_id":"sha256:0fe571d8e7bbfe79a5a0ebe01b6c0045fff2520ee1db1a86bcd210ba87225211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W4ITPBL266ORXAVR4HLM5ODG2T/bundle.json","state_url":"https://pith.science/pith/W4ITPBL266ORXAVR4HLM5ODG2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W4ITPBL266ORXAVR4HLM5ODG2T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T08:40:44Z","links":{"resolver":"https://pith.science/pith/W4ITPBL266ORXAVR4HLM5ODG2T","bundle":"https://pith.science/pith/W4ITPBL266ORXAVR4HLM5ODG2T/bundle.json","state":"https://pith.science/pith/W4ITPBL266ORXAVR4HLM5ODG2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W4ITPBL266ORXAVR4HLM5ODG2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:W4ITPBL266ORXAVR4HLM5ODG2T","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7b71372d576f02718bccbaa5a4335d2ff179348ae89a0199705fad76b970f5d7","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2007-03-07T16:00:51Z","title_canon_sha256":"e86ca58747a80ac7bb25f6b9f2ef9d76c8a5f0211056bd06d41b6dd4f6eada72"},"schema_version":"1.0","source":{"id":"quant-ph/0703060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0703060","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0703060v1","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0703060","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"W4ITPBL266OR","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"W4ITPBL266ORXAVR","created_at":"2026-07-04T15:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"W4ITPBL2","created_at":"2026-07-04T15:31:51Z"}],"graph_snapshots":[{"event_id":"sha256:0fe571d8e7bbfe79a5a0ebe01b6c0045fff2520ee1db1a86bcd210ba87225211","target":"graph","created_at":"2026-07-04T15:31:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0703060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper we discuss two different types of language ","authors_text":"A. Doering, C.J. Isham","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-03-07T16:00:51Z","title":"A Topos Foundation for Theories of Physics: I. Formal Languages for Physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0703060","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:488c36da8cba7c390c37a22b622399a8713622b1b4281320321af000174b28cb","target":"record","created_at":"2026-07-04T15:31:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7b71372d576f02718bccbaa5a4335d2ff179348ae89a0199705fad76b970f5d7","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2007-03-07T16:00:51Z","title_canon_sha256":"e86ca58747a80ac7bb25f6b9f2ef9d76c8a5f0211056bd06d41b6dd4f6eada72"},"schema_version":"1.0","source":{"id":"quant-ph/0703060","kind":"arxiv","version":1}},"canonical_sha256":"b71137857af79d1b82b1e1d6ceb866d4f45bb8ff80081988ea93eb3d96d8f9c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b71137857af79d1b82b1e1d6ceb866d4f45bb8ff80081988ea93eb3d96d8f9c1","first_computed_at":"2026-07-04T15:31:51.821528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:31:51.821528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EheGHuIUmUiw2/m0Pwy/FxG4kHQF2CMoHtnIgyk/3rpAUuo/O8c/GsbNFzfV5IaRHn+pQYWP9pQ6eb8DX0SWAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:31:51.821947Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0703060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:488c36da8cba7c390c37a22b622399a8713622b1b4281320321af000174b28cb","sha256:0fe571d8e7bbfe79a5a0ebe01b6c0045fff2520ee1db1a86bcd210ba87225211"],"state_sha256":"147293f3db8b2df21ee4b131f1a4357bd7c3e7cb0f35a831925bd3fff1e44dc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KU+c7qlZh47FEOm6LU1gW51kIaX8Bm5bg2HmEwRPRsmgODXOMKQucMlHAs47QI9P0ZYlaLCmpQR8y0IqE1oGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:40:44.906170Z","bundle_sha256":"3f22a16b4be7e4df4f06248b0920ba25ef2af30c79f059a07dfeb3bb4a04e223"}}