{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NQSA6JKT2LBH22UE6GJEY4LTO7","short_pith_number":"pith:NQSA6JKT","canonical_record":{"source":{"id":"0910.2415","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-13T18:55:52Z","cross_cats_sorted":["math.DS","math.LO"],"title_canon_sha256":"0aa29573ffd85234389db5da43ea573353500d3f75e8de87d28b68cc89f17efa","abstract_canon_sha256":"cf719276f836e25109ce0a3d7f4a30bc7c04a0802dac42f336485bbd6e164daa"},"schema_version":"1.0"},"canonical_sha256":"6c240f2553d2c27d6a84f1924c717377da9bd29aeb70fcf6064e1bd49bcf44a3","source":{"kind":"arxiv","id":"0910.2415","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2415v7","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"NQSA6JKT2LBH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NQSA6JKT2LBH22UE","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NQSA6JKT","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NQSA6JKT2LBH22UE6GJEY4LTO7","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2415","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-13T18:55:52Z","cross_cats_sorted":["math.DS","math.LO"],"title_canon_sha256":"0aa29573ffd85234389db5da43ea573353500d3f75e8de87d28b68cc89f17efa","abstract_canon_sha256":"cf719276f836e25109ce0a3d7f4a30bc7c04a0802dac42f336485bbd6e164daa"},"schema_version":"1.0"},"canonical_sha256":"6c240f2553d2c27d6a84f1924c717377da9bd29aeb70fcf6064e1bd49bcf44a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:12.431841Z","signature_b64":"DBkBtK1cvwAIpAeLklsA0z9GYNkjZBikt0Vg5a28Tn2PTNNa5oofGh0S/Ttd0GglK05Ehh/OvsloCWvf37coBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c240f2553d2c27d6a84f1924c717377da9bd29aeb70fcf6064e1bd49bcf44a3","last_reissued_at":"2026-05-18T02:32:12.431427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:12.431427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2415","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgcI3MDHBkaGTcXqAYGEEYJK6lNO4vF/V4dWCO91oWHO9uklAvF7BSkATjHCm4dhLCNWsNmKb1vMP1bQ0rZTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:36:07.225912Z"},"content_sha256":"54701990329d69a6b4f16fc1fa4a3a1ecf57f2badf69fffba43fa9d0326257c0","schema_version":"1.0","event_id":"sha256:54701990329d69a6b4f16fc1fa4a3a1ecf57f2badf69fffba43fa9d0326257c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NQSA6JKT2LBH22UE6GJEY4LTO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed-point tile sets and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.LO"],"primary_cat":"cs.CC","authors_text":"Alexander Shen (LIF), Andrei Romashchenko (LIF), Bruno Durand (LIF)","submitted_at":"2009-10-13T18:55:52Z","abstract_excerpt":"An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. This construction it rather flexible, so it can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2415","kind":"arxiv","version":7},"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":"2026-05-18T02:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PV6CtDVIfAZ6ega5eskvRmYpUUfJ77l+w89eAN1U4Tv21W+CaBKXJbVxjP6RcW60TQ6PmtLNyA42M42022pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:36:07.226561Z"},"content_sha256":"aa46b487a0aaf70bdf6252fcda612f4126ed83e994f202db1840d1a86a2f924f","schema_version":"1.0","event_id":"sha256:aa46b487a0aaf70bdf6252fcda612f4126ed83e994f202db1840d1a86a2f924f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/bundle.json","state_url":"https://pith.science/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/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":"2026-06-24T14:36:07Z","links":{"resolver":"https://pith.science/pith/NQSA6JKT2LBH22UE6GJEY4LTO7","bundle":"https://pith.science/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/bundle.json","state":"https://pith.science/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQSA6JKT2LBH22UE6GJEY4LTO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NQSA6JKT2LBH22UE6GJEY4LTO7","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":"cf719276f836e25109ce0a3d7f4a30bc7c04a0802dac42f336485bbd6e164daa","cross_cats_sorted":["math.DS","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-13T18:55:52Z","title_canon_sha256":"0aa29573ffd85234389db5da43ea573353500d3f75e8de87d28b68cc89f17efa"},"schema_version":"1.0","source":{"id":"0910.2415","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2415v7","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2415","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"NQSA6JKT2LBH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NQSA6JKT2LBH22UE","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NQSA6JKT","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:aa46b487a0aaf70bdf6252fcda612f4126ed83e994f202db1840d1a86a2f924f","target":"graph","created_at":"2026-05-18T02:32:12Z","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":"An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. This construction it rather flexible, so it can be ","authors_text":"Alexander Shen (LIF), Andrei Romashchenko (LIF), Bruno Durand (LIF)","cross_cats":["math.DS","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-13T18:55:52Z","title":"Fixed-point tile sets and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2415","kind":"arxiv","version":7},"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":"sha256:54701990329d69a6b4f16fc1fa4a3a1ecf57f2badf69fffba43fa9d0326257c0","target":"record","created_at":"2026-05-18T02:32:12Z","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":"cf719276f836e25109ce0a3d7f4a30bc7c04a0802dac42f336485bbd6e164daa","cross_cats_sorted":["math.DS","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-13T18:55:52Z","title_canon_sha256":"0aa29573ffd85234389db5da43ea573353500d3f75e8de87d28b68cc89f17efa"},"schema_version":"1.0","source":{"id":"0910.2415","kind":"arxiv","version":7}},"canonical_sha256":"6c240f2553d2c27d6a84f1924c717377da9bd29aeb70fcf6064e1bd49bcf44a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c240f2553d2c27d6a84f1924c717377da9bd29aeb70fcf6064e1bd49bcf44a3","first_computed_at":"2026-05-18T02:32:12.431427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:12.431427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DBkBtK1cvwAIpAeLklsA0z9GYNkjZBikt0Vg5a28Tn2PTNNa5oofGh0S/Ttd0GglK05Ehh/OvsloCWvf37coBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:12.431841Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2415","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54701990329d69a6b4f16fc1fa4a3a1ecf57f2badf69fffba43fa9d0326257c0","sha256:aa46b487a0aaf70bdf6252fcda612f4126ed83e994f202db1840d1a86a2f924f"],"state_sha256":"c315d985001d53a753b03eabf33df0acd4b53229f2de1a4d8965f5b835d596b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hD/Pnqu2EUw9aGuneYffb1K0ok0XuOyii8n+npIEZL3/p4yYJutHPcZOjQOfIFAnQpeoNC74QuZIVRAzNM40BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:36:07.229646Z","bundle_sha256":"7bf18f8ca4ae0e32cc94b991b4689cbfbcf9bb3570b5fda683d2d1d736925dac"}}