{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:IXKPWILPODONK3EXBVQCGL3F77","short_pith_number":"pith:IXKPWILP","canonical_record":{"source":{"id":"math-ph/0507017","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-07-07T08:09:56Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"774a1c83b1df0fb66940d87b22008bc54f8738e2cf077d7a428d014eb3cb5fa8","abstract_canon_sha256":"aab8eae1ecc9cd58d37de318187fd8c540b409c6b1f5b23dc0b9dd87bd0b20e9"},"schema_version":"1.0"},"canonical_sha256":"45d4fb216f70dcd56c970d60232f65ffc1a48b14e72c43c1f61be469b5069e02","source":{"kind":"arxiv","id":"math-ph/0507017","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0507017","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0507017v2","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0507017","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"IXKPWILPODON","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"IXKPWILPODONK3EX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"IXKPWILP","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:IXKPWILPODONK3EXBVQCGL3F77","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0507017","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-07-07T08:09:56Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"774a1c83b1df0fb66940d87b22008bc54f8738e2cf077d7a428d014eb3cb5fa8","abstract_canon_sha256":"aab8eae1ecc9cd58d37de318187fd8c540b409c6b1f5b23dc0b9dd87bd0b20e9"},"schema_version":"1.0"},"canonical_sha256":"45d4fb216f70dcd56c970d60232f65ffc1a48b14e72c43c1f61be469b5069e02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:54.544295Z","signature_b64":"f4c1TOAN3CtOt8ATiTpbmtOuWR1qfBnqRJ5d2X0dNXfH2KwBhkRmctVm/EwBFUjp4zAulnLrHRfN87rQtwNpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45d4fb216f70dcd56c970d60232f65ffc1a48b14e72c43c1f61be469b5069e02","last_reissued_at":"2026-05-18T04:17:54.543756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:54.543756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0507017","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ay+2LFBzfUeeTBd+F5tVahXjYRn3oLNoiFLXVS7r2MKFpBoTBV5SuGIBO0VuNbqG1SXN/dQH7bYUS+RU+f6cBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:59:46.656852Z"},"content_sha256":"2fc9d9e3463b9699c904e61668f63591f73774060232f256bc05a0ff3f7bd318","schema_version":"1.0","event_id":"sha256:2fc9d9e3463b9699c904e61668f63591f73774060232f256bc05a0ff3f7bd318"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:IXKPWILPODONK3EXBVQCGL3F77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Continuum Limit of Discrete Geometries","license":"","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Manfred Requardt","submitted_at":"2005-07-07T08:09:56Z","abstract_excerpt":"In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework within the category of general metric spaces by combining recent work of our own and ingeneous ideas of Gromov et al, developed in pure mathematics. A central role is played by two core concepts. For one,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507017","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HKjAQWvM1hzxB6eEIwKRR8J6k89Z1BTh7FljgIgujLXq3xz4lAbk6q4ucgOzfDsFvbdT4blgx6Lhu9/BWHUXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:59:46.657206Z"},"content_sha256":"eadc5a20dc192ea433d10a0cb979a5cfe243bfd8be0cb963d71be4aa36b3319c","schema_version":"1.0","event_id":"sha256:eadc5a20dc192ea433d10a0cb979a5cfe243bfd8be0cb963d71be4aa36b3319c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXKPWILPODONK3EXBVQCGL3F77/bundle.json","state_url":"https://pith.science/pith/IXKPWILPODONK3EXBVQCGL3F77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXKPWILPODONK3EXBVQCGL3F77/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":"2026-06-30T04:59:46Z","links":{"resolver":"https://pith.science/pith/IXKPWILPODONK3EXBVQCGL3F77","bundle":"https://pith.science/pith/IXKPWILPODONK3EXBVQCGL3F77/bundle.json","state":"https://pith.science/pith/IXKPWILPODONK3EXBVQCGL3F77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXKPWILPODONK3EXBVQCGL3F77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:IXKPWILPODONK3EXBVQCGL3F77","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":"aab8eae1ecc9cd58d37de318187fd8c540b409c6b1f5b23dc0b9dd87bd0b20e9","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-07T08:09:56Z","title_canon_sha256":"774a1c83b1df0fb66940d87b22008bc54f8738e2cf077d7a428d014eb3cb5fa8"},"schema_version":"1.0","source":{"id":"math-ph/0507017","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0507017","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0507017v2","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0507017","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"IXKPWILPODON","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"IXKPWILPODONK3EX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"IXKPWILP","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:eadc5a20dc192ea433d10a0cb979a5cfe243bfd8be0cb963d71be4aa36b3319c","target":"graph","created_at":"2026-05-18T04:17:54Z","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"},"paper":{"abstract_excerpt":"In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be constructed from a more primordial and basically discrete underlying substratum, which may behave in a quite erratic and irregular way. We develop such a framework within the category of general metric spaces by combining recent work of our own and ingeneous ideas of Gromov et al, developed in pure mathematics. A central role is played by two core concepts. For one,","authors_text":"Manfred Requardt","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-07-07T08:09:56Z","title":"The Continuum Limit of Discrete Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507017","kind":"arxiv","version":2},"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":"sha256:2fc9d9e3463b9699c904e61668f63591f73774060232f256bc05a0ff3f7bd318","target":"record","created_at":"2026-05-18T04:17:54Z","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":"aab8eae1ecc9cd58d37de318187fd8c540b409c6b1f5b23dc0b9dd87bd0b20e9","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-07T08:09:56Z","title_canon_sha256":"774a1c83b1df0fb66940d87b22008bc54f8738e2cf077d7a428d014eb3cb5fa8"},"schema_version":"1.0","source":{"id":"math-ph/0507017","kind":"arxiv","version":2}},"canonical_sha256":"45d4fb216f70dcd56c970d60232f65ffc1a48b14e72c43c1f61be469b5069e02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45d4fb216f70dcd56c970d60232f65ffc1a48b14e72c43c1f61be469b5069e02","first_computed_at":"2026-05-18T04:17:54.543756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:54.543756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4c1TOAN3CtOt8ATiTpbmtOuWR1qfBnqRJ5d2X0dNXfH2KwBhkRmctVm/EwBFUjp4zAulnLrHRfN87rQtwNpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:54.544295Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0507017","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fc9d9e3463b9699c904e61668f63591f73774060232f256bc05a0ff3f7bd318","sha256:eadc5a20dc192ea433d10a0cb979a5cfe243bfd8be0cb963d71be4aa36b3319c"],"state_sha256":"2e1739093df53d7b81a79f5d2c8335942d05215ec857e5eededfac49e735e16c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JUcMurFONfMEJN4OeZk27fYbUr9sXruUtuQKxHoDjpuWvGMzD71gDeRnyfXr6bPkHHmwdVE3asiO4hYLcvmcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T04:59:46.659590Z","bundle_sha256":"5efdaa891a036592ca9df02e0ec115a6323b9d1c48119f0f2b658a560935e3dc"}}